You can do forward secrecy if you don't need to remember the old session keys (e.g. in SSL) but I don't see how to do it if you want to have a folder full of DMs.
Discussion
Afaik 0xchat does this by creating ephemeral keys that are then stored to be able to decrypt old messages. If any of the keys are leaked, then only a subset of the messages can be decrypted (I'm not sure how many, might be just one). But then this also goes the other way: if you don't have access to those keys anymore, then your DMs are gone. I guess it's just a matter of tradeoffs.