If you are adding the messages to an IMAP account, then yes it should be adding the messages to the mail server.

Did you select a folder under "Local Folders" before you started the import to explicitly tell the tool where to import. Or did you just select the option and hope it would work it out correctly. (we see lots of the latter. Mostly as complaints the tool is "greyed out" because nothing is selected to import to, but the wrong import location is just as easily selected.)

It's indeed an IMAP account. I could not find a way to change the account settings from IMAP to POP so I deleted it and recreated the account. With the POP settings importing messages was a lot faster but it stopped at 4500 (I selected 23000 messages). It refuses to import more messages. If I try it says 'importing messages, please wait...' and then nothing. Is this a known limitation? The folder I'm trying to add these messages to is the inbox of the email account.

Was eml the only option open to you? That's an awful lot of discrete messages to handle.

It would be much smoother to copy a file/folder into the profile using your file manager, so it is a simple file copying operation, rather than an email protocol based activity, but this mandates that you have an mbox file, and of course about the only place this would come from is another installation of Thunderbird.

I take it that you are not importing from another Thunderbird?

I'd split the old eml files into multiple folders (for ease of management), then import folder by folder. It looks like 4000 per folder might work.

You're quite a long way off piste with this one. I doubt there are many users with experience of moving such a large number of messages, so I doubt there is any practical exposure to whatever limiting condition it is that you have run into.

email programs offer folders other than the inbox for mail storage for very good reasons. I suggest you use folders other than the inbox.

Using the inbox to store all your mail is like parking your car in the verge of the freeway with the keys in it. Something bad will happen and it is only a matter of time. The inbox is a very busy place with mail being added and removed and with new virus downloads landing there first. So like parking your car, leaving mail in the inbox is really a very bad idea, unless you want your car stolen or in this case your mail lost do to some unlikely collision of events.

My guess is you have an anti virus program that is scanning your profile folder. Try disabling that animal and you might have more luck, if you see time out messages, click the continue button. It is truly amazing how many people click the stop button and then complain that it stopped working. The tools were designed to move a few emails around. Not migrate a decade old archive, so they will be slow and they will be very slow if Thunderbird is online and even slower if you have an anti virus program scanning the store every time a few emails are added.

Finally I suggest you import your mail to the inbox on local folders as you are probably not using that. You can move things around later, but importing to an active account is not really a good idea.