OK. I don't want to tempt fate, but I may have discovered what the issue is. SiTech offers you the opportunity of building and then using a horizon file. I have built such a file and normally have it switched on. My 'Park' position is almost certainly a little below that horizon. SiTech doesn't seem to mind this (indeed I can set 4 Park positions - I have one that points at my LED flats panel which is obviously well below the horizon).
SGP seems not to like the horizon file. Indeed, I noticed that with the horizon enabled I could Unpark the mount but it would quickly offer me the 'Unpark' option again.
So I unticked the horizon file in SiTech and tried again. Unpark and Park worked every time (I probably tried it a dozen times). Each time, though, there was a delay of around 10 seconds between issuing the Park command and the mount actually beginning to move. I'm not sure what is to be gained by having a delay - SiTech and Maxim are immediate.
I tried replicating the problem by selecting SiTech and POTH as my telescope. It didn't seem to make any difference. With the horizon file turned on, the mount is unreliable in Park. With the horizon off, both SiTech and POTH parked and unparked normally (but with the same delay).
I hope this is helpful to people.
Now I have two issues to solve:
1) How do I stop SGP following a target below my horizon? (Is there a 'minimum altitude to image' feature?)
2) Is there a way of confirming that the mount is parked before I take the big step of closing the roof?