Well since you say you have 3.23's I'm assuming you have the 4L60E (4 spd auto). This trans sucks. I dunno how else to say that. I have had mine since Sept. 1999 and it now has 115k on it. The transmission slips in 2nd gear at WOT. Before you say that's a long time, realize I live at 5500 ft. above sea level so the trans isn't seeing the full fury of even a stock LS1. It's probably losing a good 50hp or so from what it would be at sea level. Heat will destroy these transmissions, so if you want it to last a long time, get a trans cooler in there asap. Depending on how many miles you have on the car you may want to get the trans flushed. I've heard horror stories of people flushing them after about 75k miles and losing gears because of it. In any case change the fluid regularly. If you run normal street tires the transmission will live a reasonably long life. However, if you go slap slicks or even drag radials on it, the forces on the trans and drivetrain go up really quickly. I've also heard of people blowing their trans bands just by letting the car shift 3-4 at WOT. But since that doesn't happen until about 135 mph anyway just take it easy
On a stock car, at sea level, with reasonable maintenance and no stupidity such as neutral drops, the trans should live a decent life. If you start modding and make much more power than stock, get stickier tires, etc, you'll go thru them like water. Same goes for rearends! The LS1 is definitely the jewel in the f-bodies drivetrain, and if you aren't careful, even a stock one will eat up the rest of it!