How do I reverse erosion which is lowering earth around fence posts?
Looks like that hill is mostly bare dirt. So, that's going to be a problem.

You've already mentioned two options: retaining wall and ground cover. If you can't do the retaining wall, I'd start with the ground cover. Find out if there are some hardy local native plants that will spread to cover and hold the earth together on that hillside for you.

If the erosion is primarily weather (rain) you could consider the ground cover along with some sort of physical barriers as well...perhaps pretreated timbers running horizontally down the side of the hill staked in. This would be a form of DIY geogrid.