I'm guessing you have a weak grip, and you aren't using any powder.
Your hands sweat, and they get "greasy". You sqeeze to tighten your grip, and the bar grinds into your flexh slowly ripping into it. You push hard against the bar, and it pushes through your soft flesh into your bones, creating callouses or worse blisters. Kind of brings you back to elementary school when you played on the jungle gym, puffing on your hands to give yourself better grip so you don't slip when you skip a few bars.
Don't wear gloves, your going to sweat into them, and your hands will gain the consistency of a raisin. Remember taking hour long baths as a kid and your fingers look like prunes, that's waht is going to happen, and when you go to let the bar down after some deadlifts your fingertips weaken and your palm is stretched to the point where it feels like your skin is going to be ripped off. You don't drop the weight though, because you don't want to be embarrassed in front of the other guys.
Work on your wrists, 20 lb kettlebells are going to do wonders for your grip. Your grip is strengthened through your forearm.
Want a demonstration of your strength?
pull your sleeve up, and open your palm face up
push down on the soft of your elbow
use a lot of pressure when you do so
keep using the same pressure as you move up your arm
flex your arm as your hand begins to feel the effect
flex your hand when you realize you are tensing your shoulder and bicep/tricep instead of your forearm.
You have to work the areas of your arm, that support your hand before you begin to worry about the strength of your hand and what it can withstand.
Your triceps should equal the strength in your biceps. your forearm should be able to curl 80% of what your dumb bell max weight is able to handle. Your wrists should be strengthened and stretched before every set.
Do some research on kettlebells, they are imho, todays most advanced grip strengthening exercisers.