At what age does a male dog become infertile?

I have a male Pomeranian 11 years old. We recently got a female Pom who is 3 years old. We don't want puppies. In the past the vet has suggested we not neuter him because he is too small to safely anesthetize. Right now we are trying to get her healthy, she came to us with ear, skin, and bladder infections and is on meds for all of that. We are planning to have her spayed when she is healthy enough to do so. My concern is I suspect she is coming into heat. I've read that male dogs stop producing sperm at around 10 years old. Is that true?