Christian,
Here are the important log entries in your log.
(Setup) 00:25:36 Pointing error is 18.238 arcmin @ angle 104.98
This is the result of all that focusing effort and finally getting to center the target perfectly. This is the point in time Bob's comment referred to.
Then your imaging started as planned, with the first three images solving correctly with the target spot on and no re-centering correction applied.
Image 1 00:37:25 Pointing error is 0.063 arcmin @ angle 10.70
Image 2 00:48:31 Pointing error is 0.066 arcmin @ angle 12.77
Image 3 00:59:32 Pointing error is 0.066 arcmin @ angle 11.89
What happened next is hard to determine. It could be a one-off issue. I think you'll never know. Perhaps, if you found the "focal length" setting in Preferences/Telescope tab was off some, as Bob suggested, then it could be close enough to some computational margin to affect the plate solution one way or the other (solved or not solved). I'm just thinking out loud. The images 3 and 4 certainly look practically identical, except as William pointed out. You would have thought it should have been solved. If you open Image 3 and Image 4 in MaxIm, you could use the Pixel Math function in the Processing menu to subtract the two and see if there's any obvious artifacts (beside the satellite trail and the cursor cross) that might spoil the plate solution.
Image 4 01:11:29 FAILED - Will skip final image solves until target changes
From then on, ACP does not try to plate solve all the rest of the images. This is a Prefences/General tab setting you can override by checking the first check box. In that case, even though you fail to solve image 4, ACP will go on to try solving image 5 and all the rest. The penalty is, in your case, about 3 seconds for each plate solve. If indeed it was just a one-off error failing to solve image 4, then the rest should solve (well, except for other one-off failures...). I think you can tolerate that extra 3-second overhead, since you were expecting to do a plate solve anyway. You might want to check that tick box.
Image 5 to Image 15 First image plate-solve failed, skip solves until target changes
Below you see that even after a flip, which generates a pointing update, the pointing update solves, with results similar to that at the beginning, yet after that ACP skips plate solving the remaining images.
Flip + pointing update 03:11:37 Pointing error is 16.546 arcmin @ angle 71.31
Image 16 to Image 35 First image plate-solve failed, skip solves until target changes
Incidentally, have you tried solving Image 4 (and the rest, for that matter) with Visual PinPoint? It, too, uses the same PinPoint engine that ACP and MaxIm use. That would be an easy and quick way to get the image center and distortion parameters.