The paint on my bicycle is damaged
I'm no expert but having repaired the paint on several cars, I would think that a week from the application of the last coat should be long enough for the paint to cure if it was applied correctly. That said I would assume one of two things:


You are clamping the frame much to tightly. I had this problem when I first bought my stand. Buying a carbon bike cured me.
The application of the paint was too hasty. Possibly the primer or one of the early coats of paint did not have time to cure and adhere as it should. This would allow subsequent layers to shift when pressure is applied.