Weird.
I'm not sure I'm following exactly. What precisely changes between the "not repeating" checks? I'm not clear if you are saying the high/low reading changes on each rotation or each time you remove and replace the indicator and base.
Pictures or a video might help to troubleshoot.
If the spindle taper isn't aligned with the bed ways, then the measured deflection will vary depending how far you measure from the headstock.
Get a sharpie and put a dot on the circumference of whatever chuck is currently on the lathe. Lock down your carriage or tailstock and put the mag base on that. Mark an outline precisely where you place the base, and don't move the tailstock/carriage. Rotate and position the indicator tip precisely over the dot and zero the dial.
Now without touching anything else, rotate the chuck. Mark an L and the reading at the low spot, and an H and the reading at the high spot.
Do the readings (high, low, and zero) change as you continue rotating? (Would indicate preload, bearing, or spindle/chuck issues)
If you remove the indicator and base, then put everything back in exactly the same positions as before (without moving the carriage/tailstock reference location and starting on the same dot) are you getting significantly different readings? (Can't imagine what would cause this, but will help to focus in on the problem).
This is really puzzling.