Like Racerbob, my Thunderbird checks for new mail on several accounts when started. Then, depending upon the account, it may check fairly often, or maybe not again.
I am not seeing the problem the OP has. Here I am running Win 7 Pro (64 bit), and the Thunderbird is 32.0 on the Beta release. Might this be some interaction between the operating system version (and update status) and version of TB?