Make sure there is not too much grease on the threads. The ground side must conduct through them. Make sure contacts and battery posts are clean.
If the above issues are not the problem, my next thoughts would be with the foam ring in the base of the light. Does it have one? Is it the large one that fits around the outside of the barrel? If it is, it might be causing contact problems with certain battery brands. On surfire 123's for instance, where the skin rolls around the battery on the base, it's pretty thick. Those two things combined would keep one of my P1's from even lighting. The foam would not compress enough to make good contact. Once I removed the foam ring from the bottom, all was well. Eveything worked as expected. You could try removing it if you have one of the large foam rings. The battery might rattle when the light is Off after that, but one layer of electrical tape around it will cure that.
On another P1 I added the small foam ring to the bottom of the light (it had no foam) and it's fine also. The small foam ring surrounds just the contact at the bottom and doesn't come near the outside edge so it doesn't add any extra thickness that needs to be compressed due to the battery skin to make good contact.
Hope this helps to solve your issues.