Lou,
That sounds like you might have a slightly bent mandrel. Check your mandrel for a bend, make sure your retaining nut at the end of the mandrel is not too tight. One method I use is to have the mandrel turning with no blanks on it. Let a pencil rest lightly on the mandrel and move it down the mandrel. If the pencil bounces, the mandrel is likely bent. Also, hard though it may be to believe, having the nut too tight or too much pressure on the mandrel with the tailstock can flex the mandrel, causing your problem.
Some beat the problem by only turning one end of the pen at a time, keeping all turning near the headstock.
FWIW,