You don't mention if other avionics or systems are effected but 10 minutes sounds like the approx. time it takes for battery voltage to drop below minimum required voltages if your generator/alternator is not on.
When I changed my aircraft (from Boeing B-314, or Lockheed Constellation, or Douglas DC-4, or Short Solent) to the default Cessna 172, the thing I noticed immediately was that the Master switch was off.
When I turned this on, stabilised everything in the Cessna and flew it on auto for several minutes, I changed back to one of the add-on aircraft, flew it on autopilot for a while, and all was okay.
However, I have a situation where I need to start with the Cessna (or any default a/c that has a Master switch) and only change to an add-on after ensuring the Master and/or the Battery switch is on.
But at least it has solved the problem and answered the question as to why the autopilot was dropping out.