I'm not aware of any software that stops working if you don't pay for maintenance/support. You should be able to use your software for as long as you want without paying the annual fees.
The issue, though, is when you find bugs in the software, and you can't get bug fixes without paying the maintenance fees. I find this to be highly unethical, but it's common with some software.
Also, the annual maintenance fee typically includes updates and new versions, so your software is always current.
The exception is subscrption based software. But that doesn't come with the big up front costs.