SpaceChef I don't get why the calibration succeeded and guided just fine for several shots then suddenly went off. But also the calibration doesn't explain the erratic behavior when the plan wasn't running and the asiair would plate solve, succeed and slew to point at the ground or wrong direction and the polar alignment was off by only off by a second.
That kind of calibration (not perfecty 90º between the blue and red lines, so I wouldn't consider it to have "succeeded") will cause declination errors to move the RA axis, and vice versa. Typically caused by doing calibrations near to the pole.
Where did you perform the guide calibration? When you take a high declination target like M81, you must first move the mount near to the celestial equator (+/- 30º is sort of OK. +/- 15) is even better) and calibrate the autoguiding parameters there. Only then slew to M81 and start autoguiding there.
slew to point at the ground or wrong direction and the polar alignment was off by only off by a second.
This is often caused by the ASIAIR losing its pier-side information after that 60º slew during polar alignment. Always home the mount right after a polar alignment session, and only then perform GOTOs (with a German mount, a GOTO with the wrong pier side will produce the effect you saw).
Do not use auto center in ASIAIR; it is not accurate enough. After turning Auto GOTO off, do a couple of "manual plate solve, "Sync & GOTO , recapture image" (rinse and repeat those three -- be sure to recapture an image after doing the "sync and GOTO") to get a more presise result from plate solving.
You can also manually do a Sync and then manually do a GOTO after, instead of using Sync and GOTO, which has bugs (like misidentifying horizon) after a plate solve.
Don't waste time with polar alignment; ASIAIR is not repeatable to 15 (or more) arcseconds (try doing two polar alignments one right after another, and you wiill see). 20 arc seconds is pretty much an overkill already for CMOS type exposure times. Check the web for polar aligment error and field rotation.
Remember, you are not using some real astrophotography software, but an ASIAIR.
Chen