Hello BP,
If removing and re-soldering the MCU then results in normal operation of the oscillator, this is suggestive that you either have a short circuit (solder bridge) or an open circuit (bad joint). Rather than removing the MCU, I think you really need to identify the actual cause in each production unit, to see if there is a common pattern.
Using a high Z oscilloscope probe at the oscillator pins of the MCU might help - these should be biased to about half Vdd. If the voltage at either pin corresponds to a supply rail, this is indicative of a problem.
I would doubt that moisture would represent an issue during factory testing. If you think that there is flux or moisture present you should be able to confirm whether this is the problem by cleaning the existing boards, and then properly drying them. Of course, the act of cleaning the board may also have an effect on an intermittent solder joint.
If you are using RoHS manufacture, identification of suspect solder joints is probably more difficult.
Regards,
Mac