The lathe tailstock uses a set screw to hold alignment while tightening the bolt underneath the tailstock. The stock set screw uses just a slotted head and its dog point isn't very well made, so when you tighten it the tailstock tends to move out of alignment. I replaced the stock screw with a socket head cap screw, and inserted a ball bearing in front of the new screw. This allow the set screw to apply much more even and stable pressure as it's being tightened.
Also, make sure you don't have any paint over spray on the tailstock's mating parts.