We've had a few requests like this - and it's something that we've spent more than a few cycles thinking about. The key for us is figuring out how to detect this scenario vs. a production scenario where you were debugging a problem with a process that has since exited, but want to keep examining the logs. This is something we want to nail to help using Loupe in a development scenario!
Our application only allows a single instance to be running at any time. When debugging, I keep having to close/re-open the live view because when I stop debugging the session is disconnected. I wish there was a ‘continuous’ live view. Showing different sessions of the same application in the same live view window.