According to my source, the maximum mileage for transmission service is 120,000 miles. For severe service, like towing, high speed driving, extremely dusty or hot conditions, the recommended service interval is 30,000 miles. I think you are due for a transmission service. 60,000 sounds like a good interval if you don't tow or drive hard.
If you want to find a specialist, here's a directory link for you: