All 'modern' CRT sets, with the exception of Sony Trinitron use PIL (Precision In Line) tubes, and the scan coils are permanently bonded to the CRT neck, I've never seen a PIL tube where the scan coils came loose. Likewise, the CRT adjustments are permanently glued in place during manufacture, and so don't tend to come loose either.
By far the most likely reason is the posistor, a device that degausses the CRT every time it's turned on from cold. These usually consist of two thermistors, one PTC and one NTC, and a common fault is that one of them cracks in half, causing the CRT to become magnetised.
So you might need to replace the posistor - or it could even be a dry joint where the posistor is soldered in the board.