Hazy/fogged plastic windows are nearly always caused by the use of paper towels which are made from wood particles which leave tiny scratches behind during each use. Instead, use only soft cotton towels, t-shirts, old clean baby diapers, etc. and a bucket of warm soapy water to clean them.
To remove scratches/hazing, it takes some serious elbow grease with multi-step plastic window polishing kits like from Novus or Meguiers. Such kits are almost never found in auto parts stores, you have to go to boating, RV, or aircraft supply stores. Plexus is an aerosol spray cleaner/final polish which is good for regular cleaning/polishing use once the windows are restored back to being clear again.
Good luck and never use paper towels again.