Threads in _chat are archived after 5 days and deleted after 9,999,999. Other threads are archived after 32 days and deleted after 9,999,999.
The exceptions are noted on the topics themselves - eg media requests aren't archived at all, but deleted after 366 days.
To find threads in the archives, just use the 'search archived messages' link above. (Just in case someone wonders how to do that...)