We have six PCs in our house running Windows 7 Ultimate that are on 24/7 with no standby or hibernation. I can assure you I've never seen a weird pop-up as you describe. It is not intrinsically coming from Windows 7, but more likely something you may have installed, or was bundled in by the maker of your PC.
You hinted that this is an HP machine. My experience with HP is that they bundle in HP specific utilities and tools that are supposed to give you a "superior customer experience". I took great pleasure blowing away the hard drive on my HP laptop and installing Windows 7 Home Premium. No more helpful suggestions about maintenance from HP.