I would try one thing. Loosen up the seat clamp. When the seatpost is in the seattube, is there any freeplay? If so, it is possible that either the seatpost is the wrong size, the seatpost is so old that it has actually grinded to a smaller size (somewhat unlikely), and/or your frame has a manufacturing defect and the inner seattube diameter is too large. It doesn't take much.
If the seatpost is snug and there is no freeplay, then I would assume that the seatclamp is not strong enough. I also like the suggestion of roughing up the seattube with a file or sandpaper.
If you do have freeplay, one suggestion is to make a shim out of an aluminum can. They are easy to cut with a pair of scissors. I suggest rounding off the corners. I have an aluminum can shim on my seattube and my seatpost no longer slips.
Also, if there is grease in your seattube, make sure that there is just enough grease to let the seattube slide in.