Whats the current draw? If the fuel pump draws more then its rated for it'll burn it out, not sure what the specs would be, but I do know that most hotwire kits come with a large relay. I think the one in my Camaro is a 40A relay but I'm not positive.
I'd bet that upgrading from a basic autozone relay to something bigger would do the trick, if it were me I'd buy a universal hotwire kit so the wiring gets upgraded as well.
A relay like this http://www.casperselectronics.com/store2/product_info.php?cPath=30&products_id=1095
or preferably this
http://www.casperselectronics.com/store2/product_info.php?products_id=675