I would definitely pour it back in a bottle and reuse it the next time I made donuts. At some point it'll get enough particulates in it that you'll want to dispose of it, but you should be able to get a few batches out of it.

reusing the oil is perfectly acceptable.  I ususally pour mine through a funnel lined with cheesecloth or a coffee filter to get the gunk out, and store it in a bottle in the fridge......everything I have read says to keep used oil refrigerated so it doesn't spoil.

I once asked a fast-food operator about this.  I was told that (fry) shortening is designed specificially for deep frying.  This means you can re-fry more times with it than if you used vegetable oil as it does not loose its viscosity as quickly.