Will petroleum jelly applied to the rubber on the outdoor power outlet help prolong the rubber life?
Vaseline, also known as petroleum jelly is a petroleum product. Unless you can be comfortable that the rubber seal will not react to petroleum based products, consider to use a silicone based product. I've used a GE product known as dielectric grease on outdoor rubber items, specifically in the cable industry. Even with extreme southern USA sunshine, ocean salt air and plenty of microbes, the rubber lasts for years. I'd think that even a silicone plumbers grease would work if re-applied as needed.