@Phaedrux
This printer has been causing me a lot of quality problems since Dec of 2019 where I sort of let it rest (small single object TPU/TPE jobs printed fine) for a year after Covid happened before putting more (but random) time in to troubleshooting it.
Over the last few years replaced all the major parts including this last week replaced the Duet2 with a Duet 3 and 1lc tool board. Once I got everything for the most part working (ie printer could print), I started working on Auto Bed Leveling again, and was again having trouble that reminded me about this post. I reread your question a few times (asking if I run leveling multiple times in a row does it get worse) thinking it was a clue. But as I never reran auto bed leveling more then once in a row, I didn't see this happen when I was testing, as the bed would get so far out of level that the BL Touch would give up or already be triggered when it went to a location to probe for the bed.
Turns out this was the problem the printer was having after I moved to the Duet 3. Every time I ran it, bed leveling got worse in the same way. Focusing on what could cause this, I realized that the Z motors were not associated with the correct locations.
I am not sure on what caused the problems with this printer on the Duet 2, but think the board is OK and it was just some calibration that got out of whack when trying to print a handful of different filaments that ended up being bad... And wasn't able to figure out what I did. Going to the Duet 3 forced me to redo everything, gave me an Accelerometer for Input Shaping and all the other goodies I get when using an SBC. So I am not complaining.
And as always. Thanks for the help!