Depending on the software, testing in new environments and adding information about this, e.g. testing server software under current distributions. If you get user reports about this, there isn't even a need to do the tests yourself.
Maybe clearly say in the README: "This project is considered stable and therefore has less activity, but is not abandoned. I promise to remove this notice if this ever changes."
I actually just encountered this yesterday on a project. It had a disclaimer that said something like "This project isn't abandoned, we just maintain 0 bugs in the bug tracker. It's stable and ready for use, and if we get a bug report we'll fix it as soon as possible"
Maybe clearly say in the README: "This project is considered stable and therefore has less activity, but is not abandoned. I promise to remove this notice if this ever changes."