Dan - sounds like the same issue I had with my car.
What I learned is that the protocol on my car's OBD2 network takes a lot longer to re-initialize after the power is cut (key off) & restored (key on). If I recall, it's ISO. The people who
don't have this problem have the newer, faster CAN protocol.
The workaround is to avoid shutting down OBD2 communication when stopping the engine. I accomplished this by installing a kill switch which interrupts the coil pickup signal on my distributor. Others have accomplished this with fuel injection interrupts as well.
Not familiar with your car so I can't offer specific advice on which path to take, unfortunately.
If you're driving a stick, you can test whether this will work for you with this very crude method (with nobody else around you, as you'll see why):
- Get yourself pointed down a hill at a slow (e.g. walking) pace, with the SG2 happily reporting data
- kill then engine by brute force: shift into a too-high gear (e.g. 4th or 5th) & briefly dump the clutch.
- make sure you quickly push the clutch in again as soon as the engine has shuddered to a stop, but
before the car comes to a halt (good luck

)
- while continuing to roll with the engine now off, watch the SG2 happily reporting data (hopefully)
It's not pretty, or particularly good for the car, but it will help you to discover whether a kill switch will work in your case.