Just because it is slipping doesn't mean that there is grease or oil on it. The disk itself has a wear surface on it, and as it wears down it gets thinner like a brake pad. The thinner it gets the less pressure the pressure plate can put on it because the springs in the plate aren't compressed as much, so that can cause slippage.

You can also increase power levels until you get some slippage. My stock clutch held down the SU's just fine, but when I went to Mikunis I had to change to an ACT clutch because it couldn't hold the power anymore.

If you aren't making a lot of power, then the likely culprit is just wear on the disk, and as said before the biggest risks are putting a lot of heat into the flywheel and/or wearing the disk down to the rivets and having them chew up the flywheel.

a little grease or oil will cause a chatter. A lot will cause a slip. You have to try really hard to get a lot on. It's very unlikely that you have grease or oil on the clutch.

If you don't accelerate hard enough to cause the slip the clutch can last a long time. So if it slips, back off. Light throttle and higher rpm are your best bet to keep slipping to a minimum. For a given acceleration level you need a given amount of HP. HP = torque * rpm (divided by 5252 if torque is in lb*ft). So for a given HP more rpm means less torque is required. I've limped a clutch or two along for quite a while using that driving technique.

Steve