...Thats like believing if you keep stabbing yourself in the leg once a day, it will eventually no longer bleed.
We're talking religion here. The faithful in some religions, mainly Christianity though, are supposed to be tested. You are not to lose your faith but have it strenghtened.
Same with Spira. They believed because they were positive their belief would eventually stop Sin form returning.
It also doesn't help that their belief wad all that kept them going. If they didn't have Yevon most would, as Yunalesca said, fall to complete despair.
When you have really nothing else to believe in you'll cling to what you have with all your might.