It's up to the author whether they want you to buy a license for each community you install it on. They have the capability to define this (and they should) in their terms and conditions that appear prior to purchase and prior to install/update. Generally without renewing you can still use the resource, but you won't get any technical support or updates for it. As mentioned though, authors can set their own terms and conditions so you should read them carefully if they are provided.
I have never known someone to reinstall a resource to fix an issue. What you would do there is contact the author for help. If they find an issue, they'll fix it and publish a new update. Of course, you would typically need an active purchase of the resource for that.
Additionally, if you maintain backups of your community you shouldn't have an issue either.
As noted, it's up to the author to define these terms as they can differ between resources. They have the ability to display their own terms & conditions prior to you purchasing or installing the resource. This was also a new capability we added with 4.5, I expect these T&Cs will be populated as files are updated.
p.s. here's what that looks like: