One thing to keep in mind about Autozone's (and similar chain auto parts stores) is that their store brand Chinese-made water pumps are, generally, shoddily constructed. Their "Lifetime Warranty" in no way means they are a high quality product, they are not. I wouldn't doubt you got one of the bad ones that so commonly make it to the store shelf.
Since my TJ gets out into the boondocks so much where I need a high degree of reliability for everything, I wouldn't run a store brand water pump. To me, there are some commonly replaced components I won't go with a store brand for.... alternators, starters, or water pumps. The slight added cost for OE quality is worth it to me.