I'm using Thunderbird 15.0.1 Windows 7 x64. I figured out the issue few updates ego.
Once I tried to turn off all add-ons, but its not helps.
I have only one POP e-mail account (and it is default), in "Server" settings checked box for "Check for new mail every 5 minutes", "Automatically download new messages", "Leave message on server", "For at most 14 days", "Until I delete them".
How to fix it?