As an FYI I was having the same issue today, some symptions:
* TOM was open overnight, tried to reply on the
Short Time Podcast thread and it said "session timed out" or something very similar.
* First thing I tried was to logout and it wouldn't let me do that, believe it said session verification failed
* So I closed my browser (FF 25.0.1) and re-opened - same issue with posting and logouts
* I do have FF reopen whatever tabs I had previously, don't know technically how that affects sessions
* In the time it took me to find this board/thread and going back to take screenshots it fixed itself. Maybe two minutes
* Never nuked my cookies
Being an owner of an SMF board myself, first thing I do for all errors is to search their incredibly helpful forums for a parallel issue. There were a few different threads, but I think
this one looks like the winner.
Assuming TOM has access to php.ini on their webhost, you would need to change
session.hash_bits_per_character from 6 to 5. I checked my board and I have it set to 5, hopefully that'll do it. That some post has a change you can edit in one of the SMF php files as well, maybe try that one if you can't access php.ini or it doesn't help.
PSA - you took the footer away from SMF 2.0.6 came out a little while ago. I think you were on 2.0.5 last time I looked, has a security update.