Steering or Rudder Issue

[Smithsonian]

My husband I purchased a 2006 Hunter 33, 3 years ago. This past summer we started having a very odd problem.
While on the helm I looked down and noticed the auto pilot rudder indicator hard to starboard. The steering wheel was in fact in that position. Sails were up, autopilot was not in use. Not knowing what returning the wheel to center would do to the direction of the boat, we started the engine and brought the steering back. The boat didnt make any hard turn both when noticed and corrected.
This would occur randomly throughout the season. I had both the autopilot system and steering checked and nothing obvious was found.
It remains a mystery, but one I find concerning.
Any ideas of what may be causing this?

[George_SD]

This is very confusing and the only idea I can come up with is slipping steering linkage somewhere - at the wheel, cables, rudder itself...

The fact that ruder reference shows a value that appears to be correct and then changing that value via input to the rudder that does not result in a change of course or other effects normally associated with a change in rudder position indicates at some sort of malfunction in steering. If it was ruder reference unit that is not connected or went bad, then changing steering input should still have impact on the boat.

I think a more thorough investigation of steering system is needed.