Summary: I have a university mailbox using IMAP protocol. My Ubuntu email clients do not download my inbox emails, not even the new ones. I can send emails though.
I use thunderbird on Windows 7 (laptop) as well as the gmail app on my android smartphone and both of them sync with the server. They both work really well.
I also set it up using Thunderbird on the same laptop with Ubuntu 14.04 (dual boot). I have recently bought a new desktop with ubuntu 15.04. Both of them do not download the inbox emails but can send emails. My inbox stay irremediably empty.
One strange thing is that it does sync with the recently sent emails, but only those sent from a Ubuntu client! So if I check my "sent" box, I can see all of the test emails I have sent with my ubuntu clients. Meanwhile I have sent "work" emails using the webmail application of my university and these ones do not appear in the sent box. I have also tried with Evolution on my desktop: same result (it can send emails, it does not download inbox emails but it downloads only emails sent with the ubuntu clients). My test email from Evolution did sync on my laptop's Thunderbird.
Note that I don't think it's a client configuration problem as I used exactly the same for Windows 7 Thunderbird and for Ubuntu 1*.04 Thunderbird. I guess it's a problem on ubuntu.
I first thought some ports are blocked, but it seems there is not such thing as a firewall on ubuntu.
mailbox configuration: SSL on port 993 with password authentification
Any thoughts? Thanks!