My cover is pretty heavy and when I remove it, I clean it with the water and pool brush on both sides, let it dry then bend it dozens of times and put it in the cover bag. The cover is about 7yr old, it's not soft and it looks like it's getting worn out where it's been bent.
guys who close my pool recommended use of some sort of chemical, which would extend the covers' life. I guess the chemical is supposed to make it softer so it doesn't get worn out as much when I put it in the cover bag. They didn't know the chemical name, they are not in selling business, but it's was something like armor all for vinyl.