No longer see messages in my inbox which I've received since May 6 2015 (btinternet?)

I use Ubuntu as my operating system, and Thunderbird for email. My inbox hasn't got any messages received since May 6. Some of the other mail folders which I have set up have a similar issue, some with no messages since March 28, while there are others which are bang up to date. I can't see any emails in my sent folder since Feb 26. This problem has only started today. I rebooted my PC but this hasn't made any difference. I can still use my email by going online - I'm with btinternet - but I was quite happy using Thunderbird. Also, there's no record of emails sent using Thunderbird when I go online, so this is unsatisfactory. I'm hoping there's an easy answer to this - help gratefully received. Regards Tim