After just a few years say 8 to 10 the rubber has been 'eaten up' by micro-organisms. Will petroleum jelly prevent that meaning prolong the life of the rubber?
The problem with rubber outside is usually UV rays from the sun. The sun degrades the material and it looks like something may be feeding on it but it is the sunlight. Power cords many times are UV resistant but not all and even UV resistant will break down over time, I found painting the cords with spray paint almost doubles the cord life at the mill where we have motors running back and forth outside. I am guessing at your problem being an outside cord because if just a seal the exposed part falling apart won’t be a problem all the work is between the parts and compressed but if concerned with this area paint would last even longer here. Note I am using a thin coat of yellow or orange for my motors barely enough to cover the black cords if I coat it thick the paint flakes off it also shows rub points in my case that we did not used to notice but do now. So try painting the rubber it has helped my motors.
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.