We found this.
They actually make clamps to hold ducts together and I believe they're quite inexpensive. But why waste $.60 when you can just duct tape everything together? When I had the vents put in the roof my coworker's husband, who works as a licensed contractor, set up the duct for the bathroom fan. He apparently decided this was the correct way to do it.
We pulled off the failing duct tape and put new duct tape in the same place. If it's good enough for a licensed contractor, it's good enough for us. What's the worst that could happen?