I have read that a rat/mouse can tread water for 3 days. :/ So that is why I never used water in the bucket. The old grease (old fish grease or chicken grease) doubles as far as them smelling the food aroma and coming to the bucket. They fight all night trying to get out and crawl the greasy walls until they tire out and kick the bucket (no pun intended). :/
From experience, they don't. I've never had one last the night.
Grease as bait is not a bad idea. From experience it is not necessary to keep them from climbing out.
Mice have very high metabolic rates. That may have something to do with why mine don't last until morning or why yours tire out so quickly. I really don't know. But I can assure you they don't tread water in there for three days.