This is exactly why I only check it twice and the second one is caught as I'm racking to the keg. The rare stuck fermentations I've had did not respond to rousing, raising the temp, adding yeast energizer (usually a combination of all three). Since the yeast were obviously not up to the task I figure it's best to get it off the stressed yeast. So ime, usually once the original pitch of yeast has stopped, it's done, it ain't going any further and racking is the next step.
As for what to do when a fermentation is stuck, ime the best methods to fix it are (in order):
Rack it onto the yeast cake of a 'good' fermentation (or add the cake to the keg). Do not aerate.
Add properly hydrated dry yeast. Dry yeast doesn't need O2 so you don't have to worry about the fact that you don't aerate (which you definitely don't want to do at that point).
After any of these had run their course I would then do closed keg-to-keg transfer.