Developers are free to change how they distribute their work at any time, which can mean changing the visibility status of the page or replacing the files with new or different ones. Generally, established pages are very rarely taken down, but there are a wide range of use cases for developers on Itch.io that can influence whether or not the developer may substantially change the page.
As an example, in many cases, people use their itch.io page as a portfolio and they can decide at any time to change the contents of their portfolio.
If you want to use someone’s work for your classroom setting and require permanent access to a particular version of a page, I recommend contacting the developer and getting permission to repurpose their work.
Hope that helps