Which size of collet?
I have two collet nuts, one for 1/2" and one for 1/4" so I don't have to keep swapping over. I think it eases the wear on the nut, too. They get an occasional spray through with carb cleaner (xylene mainly), followed by WD40, and in the winter a bit of liberon lubricating wax. So far I've not had the problem you describe, but it's only wever lightly used.
I think I'd clean the shaft's receiving cone with some carb cleaner, then very gently some fine emery paper wrapped round a little finger, and pop the collet out of the nut too, to check it too is clean. Signs of wear ought to be obvious. If there are signs, I'd replace the collet, as it might damage the shaft's cone otherwise, which would be expensive.
Is there any possibility someone's been doing it up without the cutter shaft completely down in the collet? Or has anyone used a cheap cutter that might have an undersized or oversized shaft? I'd guess that if the collet has been distorted somehow that would do it. If so, you've probably got little choice but to replace collet and nut and hope the cone isn't damaged, as there's no easy fix for that.
E.
PS: I got fed up with squinting along the table top at mine, trying see the 'benchmark' symbol or guess if I had the cutter at the right height. So I cut off a slug of 1/2" dowel, which now lives in the shaft under the collet as a depth stop for the cutter shanks. It saves a lot of fuss. It has to come out when I use the 1/4" collet, as that's a different length.