"Chris said it's a serious issue, it could damage the autopilot even if the AP is turned off.Some thoughts " I would say this COULD be serious issue, in your case I do not think it is since it has not failed in 10 years.

I can think of 3 area that the SSB could be causing this problem, there are probably more.

1 The ground/power of the SSB (SSB pulls lot of current) or the SSB is putting lots of RF on the ground/power wires and that is getting into the Autopilot.
As someone said there are filters that you can put on all the wires to and from the SSB and Autopilot. Also you could try to adding more GND/Power wires for both. Do not use the same circuit for both.

2 The SSB when transmitting put out a lot of magnetic waves that are being picked up by the wiring( acting like an antenna) of the Autopilot.
Move any SSB wires away any Autopilot wires, cover all Autopilot wires with a shield tied to ground.

3 The SSB when transmitting put out a lot of magnetic waves and are being pick up by the compass of the autopilot.
Increase distance between anything to do with the SSB and the Autopilot compass.