I went down the rabbit hole and finally came back up... It's obvious that cables are important, I have one of these:
I tried lots of things; the thing that finally appears to have helped is plugging the mDP cable in to the other port on the Surface dock; looking at the dock from the front I see from left to right; an ethernet port, a 3.5mm sound jack, mDP1 and then mDP2. If I use mDP1 I appear to get much more robust behavior than using mDP2. I hope this helps others? I put electrical tape over mDP2 to try and avoid repeating this issue!
I'll also note that dock firmware is up to date as is the surface. I can now power off the monitor, disconnect the dock cable etc. and appear to get consistent results. Phew!