plug-in updates have stopped working

I have three WP sites (each with its own domain/hosting) running on the same hosting service. Recently, one of my sites has been having problems with automatic updates of plug-ins and WP.

When I try to update a plug-in using the automatic feature, I get this:

“An error occurred while updating [name of plug-in]. Could not remove the old plug-in.”

This is not occurring on my other two sites.

I am able to update by deactivating and erasing the old version of a plug-in and then reinstalling.

I was able to update WP to the current version manually.

Any ideas what might be going on?

Thanks!