Headset/Stem problem.

The stem will only slip if it is loose, not necessarily your headset..
It sounds like you have a threadless setup and are not clamping the stem to the steerer, but only tightening the top-cap (which is ONLY meant to pre-load the bearings).
Threadless:

1. Loosen these bolts (or similar) which clamp the stem to the steerer tube.
   
   
2. Adjust the pre-load (using the top allen bolt) till the headset is as you desire.
   
3. Tighten the bolts to clamp the stem to the steerer.
   
4. profit.