We have laminated one side of it so they can still see that it is the original card.
Another option would be to bring the one you have back - if it's falling apart, it will be obvious why you need a new one.
Our GAC has always been just for a week (that is all we need...no annual passes, just one trip a year usually.). Anyway, last trip it got soaked from rain about half way thru the week and the stamps weren't even legible.I just went to Guest Services and there was no problem getting it replaced.