Why does the SARS-CoV2 virus not remain infectious forever? Or does it?
Would it help to think a little differently? Rubber bands (for example) aren’t alive either, but there are several ways they can be destroyed, including physically pulling them apart or just by having them exposed to air enough. Viruses are the same, conceptually.

Soap works in part by dissolving the layer of fat that keeps the virus together. It also ends up surrounding dirt so that it doesn’t stick to your skin and can be washed away with water. (These mechanisms take some time to work so that’s why people are recommended to wash their hands for 20+ seconds.) 

As for when a virus is just on a surface, logically we know that how long a virus remains viable depends on both the air and the surface because the science reports different numbers depending on what the humidity is and what the surface is like. One helpful source notes:


  Similar molecules appear to interact more strongly with each other than dissimilar ones. Wood, fabric and skin interact fairly strongly with viruses.
  
  Contrast this with steel, porcelain and at least some plastics, such as Teflon. The surface structure also matters. The flatter the surface, the less the virus will “stick” to the surface. Rougher surfaces can actually pull the virus apart.
  
  The surface of fibers or wood, for instance, can form a lot of hydrogen bonds with the virus.
  
  In contrast, steel, porcelain or Teflon do not form much of a hydrogen bond with the virus. So the virus is not strongly bound to those surfaces and is quite stable.