Thanks for the advice, everyone. We got Tigger to the vet and as it turns out his kidneys are starting to show signs of slow failure. :(

He was also slightly anemic and has quite a bit of arthritis in his hips (which we already suspected at age 15). He's going to be on some medication and special renal-friendly food.

I've been through this before with other cats, so I know what's coming. It sure doesn't make it any easier. *sad*