I can't replicate or even understand what you are describing. First, let's not confuse Installation with Activation, they are completely separate things that don't have anything in common and are completely unrelated.
Of course, they are shown in different spaces of the installer interface, and that is precisely so you won't confuse them.
- If you uninstall a product, you will NOT lose your activation, which is stored in Windows, and can be lost only if you reinstall Windows or you change major hardware components, like the CPU.
- If you lost your activation because of an hardware change, the product won't be uninstalled because of that, unless you uninstall it explicitly, if you need to reactivate after an hardware change, click the "Activate" button, and will reactivate a product that is still installed, but lost the activation for any reason.