Yes, I'm suggesting that you work the tree at a slightly different angle. Gaffs that are sharp(not over sharp) will kick out like a dull gaff if you are constantly moving or standing with them pointed straight downward. They ride straight downward through the wood that you are gaffed into. As you angle back a bit, your points will point inward into the tree more. Now the weight you are putting into them is being driven more inward into the tree and not downward as much towards the ground. When you ascend, try, if you can not to keep your body completely parallel with the trunk of the tree or in some cases of newbies, the climbers ass will protrude out off the tree and their chest and chin will be touching/hugging the tree. No good. Sometimes you'll have to ascend somewhat parallel with the tree. Especially if you are battling a little to drag/flip your lanyard up the back of the tree because of rough bark or nubs. In that case, you'll eventually get the feel as you take each step for whether you gaffed into a little meat or stayed too close to the surface and will slip out.
Even after you get past this hurdle and become more fluent, you'll still gaff out here and there. It will startle you less and less. It still wakes me up good if I gaff out while running a saw. Especially a climbing saw. I'm usually snugged into my climb line and lanyard when cutting so it doesn't happen much. But occasionally I get complacent and make a quick cut on just my lanyard. Usually if Im nipping a small limb out of my way to ascend up the tree. That's about when ill ride the bark express a few inches downward and remember quickly what that silly rope snapped on the back of my saddle was intended for.