I fly in the BPT with various customers; since I have a 540, I am often assigned to fly with our customers who also have this navigator. 

So I have observed this behavior with a variety of GPS Steering adapters: S-Tec 901, Aspen, G-500, and the DAC in my airplane. 

The GPS Steering performs flawlessly up to the FAF; during holds, etc.   All except inbound from the FAF to the end of the runway where it will be offset up to a half full scale needle deflection.   It makes no effort to make a correction -- as if it is satisfied.  No flags or flashing GPSS lights.   Not always off in the

same direction.  If I intentionally over power the AP, it will return to the same incorrect position.

This is not a problem with the magenta line or the D-bar needle:  If coupled with normal approach mode, it lines up with the runway flawlessly.

This happens on about half of all the GPS approaches I've tried.  One example is KGXY rwy 28.  The

amount of the offset varies but the airplane moves over to a more or less parallel course and flies that inbound.

I have not seen this behavior on the all Garmin setups except on one occasion.

Anyone?  Very frustrating.

Bill Hale.  Bonanza & Baron Pilot Training CFII