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Sometimes, as pets age, their urinary sphincter muscles don't work as well as they used to, especially when they are sleeping. Since he is dripping, I feel even more inclined to think this. If this is the case, there are medications that can help to improve sphincter tone. You should talk with your vet about them.
Also, urinary incontinance can be a sign of a disc or back problem so you will want to have this checked by the vet as well.
Let me know if you still have questions.
You are correct. It does have a lot to do with age. Since your vet has ruled out crystals and UTI's, I would talk with him about the medication to strengthen the urinary sphincter.
I hope this helps!