The metal bead on my tire seems to have come out of the fabric in one spot, and so the tire no longer stays in the rim. Is it possible to fix this, or do I need to get a new tire?
Unfortunately, if the bead is popping out, you're going to need a new tire. Your tube could have a blow out through the gap. You may want to inspect your brakes and make sure they were not rubbing on the tire. This could be causing pre-mature wear around the edge of the tire near the bead.