I didn't want to jack the topic below so I'll start this one. I'm looking for some thumb tape that has a little better grip and last longer then the usual white tape all the shops around here seem to only carry. something grippy and thin and lasts longer then a game,Thanks!
Thinness/thickness:
White tape is more grippy, the rougher it is. The rougher it is, the higher the tiny mounds are going to be. It's like abrasive pads and sandpaper, the rougher it is, the thicker it is.
So you normally are not going to find very grippy white thumb hole tape to be thin.
One of the grippiest I know of, Alligator tape, is one of the thickest.
Many of the manufacturers do make a rougher & thicker white tape version of their stock tape. But they are all ticker, not thin like black tapes.
Lasting more than one game:
I have never had any thumb hole tape last less than a full 3 game set. Every one does. (Tape you put on your thumb may not last a long time.)
So, I suspect either your thumb hole is not clean when you put the tape inside it, or you're not putting the whole piece about 1/4" below the level of the bevel. All these tapes stick fairly well. Maybe you're rolling a corner of the tape (Almost all precut thumb tapes come with the top portion rounded, to help prevent such rolling.