https://support.mozilla.org/en-US/kb/cannot-receive-messages

I've tried changing the password and have checked the server settings, but to no avail!...

Do you get any error message?

Can you post your Troubleshooting Information? At the top right of the Thunderbird window, click the menu button , then select Help, and then Troubleshooting Information. Press the Copy text to clipboard button and paste the information into your reply.

I click 'Get Messages' and it says 'No messages to download'. I can see new messages using other e-mail programs.

Troubleshooting Information?

Application Basics

   Name: Thunderbird
   Version: 38.4.0
   User Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:38.0) Gecko/20100101 Thunderbird/38.4.0
   Profile Folder: Show Folder

             (Local drive)
   Application Build ID: 20151119061742
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Memory Use: about:memory

 Mail and News Accounts
   account2:
     INCOMING: account2, , (none) Local Folders, plain, passwordCleartext

   account3:
     INCOMING: account3, , (pop3) mail.btinternet.com:110, plain, passwordCleartext
     OUTGOING: mail.btinternet.com:25, plain, passwordCleartext, true

 Crash Reports
   http://crash-stats.mozilla.com/report/index/bp-896a4d94-5936-49d4-a31d-a17842151103 (03/11/2015)
   http://crash-stats.mozilla.com/report/index/bp-36ae4821-6445-442a-9975-3a71d2151029 (29/10/2015)
   http://crash-stats.mozilla.com/report/index/bp-9e7064a9-5343-48b3-93ff-458892151027 (27/10/2015)
   http://crash-stats.mozilla.com/report/index/bp-93e989b2-3baf-4fce-a110-78c572150919 (19/09/2015)
   http://crash-stats.mozilla.com/report/index/bp-edac2e0b-5fff-49c1-b662-0575d2150908 (08/09/2015)

 Extensions
   Lightning, 4.0.4, true, {e2fda1a4-762b-4020-b5ad-a41df1933103}

 Important Modified Preferences

   Name: Value

     browser.cache.disk.capacity: 358400
     browser.cache.disk.smart_size_cached_value: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     extensions.lastAppVersion: 38.4.0
     font.internaluseonly.changed: false
     font.name.monospace.el: Consolas
     font.name.monospace.tr: Consolas
     font.name.monospace.x-baltic: Consolas
     font.name.monospace.x-central-euro: Consolas
     font.name.monospace.x-cyrillic: Consolas
     font.name.monospace.x-unicode: Consolas
     font.name.monospace.x-western: Consolas
     font.name.sans-serif.el: Calibri
     font.name.sans-serif.tr: Calibri
     font.name.sans-serif.x-baltic: Calibri
     font.name.sans-serif.x-central-euro: Calibri
     font.name.sans-serif.x-cyrillic: Calibri
     font.name.sans-serif.x-unicode: Calibri
     font.name.sans-serif.x-western: Calibri
     font.name.serif.el: Cambria
     font.name.serif.tr: Cambria
     font.name.serif.x-baltic: Cambria
     font.name.serif.x-central-euro: Cambria
     font.name.serif.x-cyrillic: Cambria
     font.name.serif.x-unicode: Cambria
     font.name.serif.x-western: Cambria
     font.size.fixed.el: 14
     font.size.fixed.tr: 14
     font.size.fixed.x-baltic: 14
     font.size.fixed.x-central-euro: 14
     font.size.fixed.x-cyrillic: 14
     font.size.fixed.x-unicode: 14
     font.size.fixed.x-western: 14
     font.size.variable.el: 17
     font.size.variable.tr: 17
     font.size.variable.x-baltic: 17
     font.size.variable.x-central-euro: 17
     font.size.variable.x-cyrillic: 17
     font.size.variable.x-unicode: 17
     font.size.variable.x-western: 17
     gfx.direct3d.last_used_feature_level_idx: 1
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     mailnews.database.global.datastore.id: 89d7a9fb-a63a-44b3-b692-3b252174a2f
     mailnews.database.global.views.conversation.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"3"},"attachmentCol":{"visible":false…
     network.cookie.prefsMigrated: true
     network.predictor.cleaned-up: true
     places.database.lastMaintenance: 1448280925
     places.history.expiration.transient_current_max_pages: 104858
     plugin.importedState: true
     print.printer_Canon_MG4100_series.print_bgcolor: false
     print.printer_Canon_MG4100_series.print_bgimages: false
     print.printer_Canon_MG4100_series.print_colorspace:
     print.printer_Canon_MG4100_series.print_command:
     print.printer_Canon_MG4100_series.print_downloadfonts: false
     print.printer_Canon_MG4100_series.print_duplex: 0
     print.printer_Canon_MG4100_series.print_edge_bottom: 0
     print.printer_Canon_MG4100_series.print_edge_left: 0
     print.printer_Canon_MG4100_series.print_edge_right: 0
     print.printer_Canon_MG4100_series.print_edge_top: 0
     print.printer_Canon_MG4100_series.print_evenpages: true
     print.printer_Canon_MG4100_series.print_footercenter:
     print.printer_Canon_MG4100_series.print_footerleft: &PT
     print.printer_Canon_MG4100_series.print_footerright: &D
     print.printer_Canon_MG4100_series.print_headercenter:
     print.printer_Canon_MG4100_series.print_headerleft: &T
     print.printer_Canon_MG4100_series.print_headerright: &U
     print.printer_Canon_MG4100_series.print_in_color: true
     print.printer_Canon_MG4100_series.print_margin_bottom: 0.5
     print.printer_Canon_MG4100_series.print_margin_left: 0.5
     print.printer_Canon_MG4100_series.print_margin_right: 0.5
     print.printer_Canon_MG4100_series.print_margin_top: 0.5
     print.printer_Canon_MG4100_series.print_oddpages: true
     print.printer_Canon_MG4100_series.print_orientation: 0
     print.printer_Canon_MG4100_series.print_page_delay: 50
     print.printer_Canon_MG4100_series.print_paper_data: 9
     print.printer_Canon_MG4100_series.print_paper_height: 11.00
     print.printer_Canon_MG4100_series.print_paper_name:
     print.printer_Canon_MG4100_series.print_paper_size_type: 0
     print.printer_Canon_MG4100_series.print_paper_size_unit: 1
     print.printer_Canon_MG4100_series.print_paper_width: 8.50
     print.printer_Canon_MG4100_series.print_plex_name:
     print.printer_Canon_MG4100_series.print_resolution: 0
     print.printer_Canon_MG4100_series.print_resolution_name:
     print.printer_Canon_MG4100_series.print_reversed: false
     print.printer_Canon_MG4100_series.print_scaling: 1.00
     print.printer_Canon_MG4100_series.print_shrink_to_fit: false
     print.printer_Canon_MG4100_series.print_to_file: false
     print.printer_Canon_MG4100_series.print_unwriteable_margin_bottom: 0
     print.printer_Canon_MG4100_series.print_unwriteable_margin_left: 0
     print.printer_Canon_MG4100_series.print_unwriteable_margin_right: 0
     print.printer_Canon_MG4100_series.print_unwriteable_margin_top: 0

 Graphics

     Adapter Description: Intel(R) HD Graphics
     Vendor ID: 0x8086
     Device ID: 0x0046
     Adapter RAM: Unknown
     Adapter Drivers: igdumd64 igd10umd64 igdumdx32 igd10umd32
     Driver Version: 8.15.10.2900
     Driver Date: 11-26-2012
     Direct2D Enabled: false
     DirectWrite Enabled: false (10.0.10586.0)
     ClearType Parameters: ClearType parameters not found
     WebGL Renderer: false
     GPU Accelerated Windows: 0

     AzureCanvasBackend: skia
     AzureSkiaAccelerated: 0
     AzureFallbackCanvasBackend: cairo
     AzureContentBackend: cairo

 JavaScript

 Incremental GC: 1

 Accessibility

   Activated: 0
   Prevent Accessibility: 0

 Library Versions

     Expected minimum version
     Version in use

     NSPR
     4.10.10
     4.10.10

     NSS
     3.19.2.1 Basic ECC
     3.19.2.1 Basic ECC

     NSS Util
     3.19.2.1
     3.19.2.1

     NSS SSL
     3.19.2.1 Basic ECC
     3.19.2.1 Basic ECC

     NSS S/MIME
     3.19.2.1 Basic ECC
     3.19.2.1 Basic ECC

If you're retrieving messages via POP for this account using other email software, make sure to tell them to 'Leave messages on the server'. Otherwise the message is removed from the server upon opening it. When you check with Thunderbird later, then the messages you expect to see may have already been removed from the server. In any case, you can check via webmail what's actually on the server.

Why should Thunderbird simply stop downloading new messages for no reason?...Nothing's changed!...Totally bizarre and VERY frustrating that I'm now forced into using Mailbird which works fine!...

Why should Thunderbird simply stop downloading new messages for no reason?

I don't know, that's what we're trying to find out. In that process you're expected to be willing to do some sort of troubleshooting, answer questions, and provide as much information about your environment as possible. If you expect a perfect solution which fixes your problem right away, then that's an illusion.

I'm now forced into using Mailbird which works fine!...

That's up to you to use another email client. But I suppose we can then stop here.

I don't WANT to use Mailbird....up until recently Thunderbird was working perfectly! I believe I have supplied you with all the info. I can, but if not please let me know as a solution to this mystery would be great!...

Have you checked the config of your other devices? Have you checked what's on the server via webmail? https://support.mozilla.org/en-US/questions/1096333#answer-811424

I appear to have solved this problem by creating an additional identical account in Thunderbird and then deleting my original account. New messages are now being downloaded so I'm keeping my fingers crossed that this continues to work!...

Good. Can you then mark your answer as 'Solution' please? Thank you.