I run into this problem often. I create a lot of throw away threads that clutter things up too much to use 'forever', so I use '24h'. Most of the time, 24h keeps things nice and tidy. But frequently I will have a long conversation about something and don't know ahead of time that it's going to be long, nor do I know that I'm going to want to keep it. I start in the evening, work on it for a while, go to bed, then to work, then dinner, chores, blah blah, and then finally get back to it and I've just missed it.
I'm going to echo the last couple replies here. Please just add a few options to the default lifetime menu and ship it. Things like a recycle bin might also work, but it's not here yet and is slightly orthogonal to the problem. You've already got the plumbing in place to allow 24 hours, just allow a few other sensible options call it a day.
The more elegant or complete solutions can ship when they ship. Perhaps we users should just be better at knowing when to preserve our chats, but the evidence clearly shows that we aren't. At the end of the day, this is two years of posts pontificating about how best to add two lines to a dropdown menu... please just fix it :-)