That looks like a Thomson post. They are sometimes a little undersized. Also, they have very little material in the column and will be crushed slightly when you crank the seatclamp down, going nowhere with the slipping problem.
At this point you should get a new post or try a different seatpost. Measure the diameter with a pair of verniers if you can and try to get a post fatter than the current one. A small difference in diameter should be all you need.
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