In terms of Roadkill, or in this case, a dog dragging up a dead rabbit, how long until saving the hide is unadvisable?

I wasn't told about the rabbit until around midnight, and it had been fetched by the dog about five pm.

I was going to retrieve the critter from the trash can tomorrow to skin and macerate it, I'm wondering if it's worth it to save the hide or not.

Generally, how long until a hide is considered not usable for tanning purposes? I suppose if the hair is starting to slip or if it smells funny or chewed up by bugs? Just wondering if there's an advisable amount of time to salvage things, as I can't seem to find a good answer.

I fleshed it a little but it's taking a while and I'm wondering if there's any better way?