Resuming a session after hitting the 5-hour limit re-bills the whole context because the cache expired, need some help.

$20-sub brokie here. When coding, I sometimes tell the agent to start a run that I know will probably burn through my 5-hour limit. The problem is that when I resume it later, the conversation has dropped out of the cache, so I have to eat the full usage for the whole conversation, even if I compact before sending the first message. Any ideas how to handle this?