[font=trebuchet ms]First, find the source of the trouble.

Make sure that you don't have too many turns wrapped around the post of the tuner. If there's a big bundle of string around the post, it will gradually let the string creep flat as the wraps tighten around the post. Bending makes this happen more noticeably.

Once you're sure the strings are installed corectly, pluck a string and then press on it between the nut and the tuner. It should go sharp, and then return to pitch when you release the pressure. If it stays sharp, the slots in the nut need to be reworked. When you bend the string, the tension increases, pulling the string tighter. When you release the bend, the tension should be reduced back to where it was, except that the nut slot pinches the string, preventing even distribution of the tension. The section between the nut and the tuner is now at higher tension, and the section from the nut to the bridge is at lower tension, re-tuning the string slightly flat. This is a fairly common problem, although it should have been set up properly by the shop before it was put on the racks. Give 'em hell.

If your guitar has a trem, you may find a similar situation with 'stored tension' between the bridge saddles and the knob end of the strings. Same solution - the guitar needs to be properly set up.[/font]