Your post just got me to thinking about my skimmer. In our previous pool, if the water got to low the skimmer would turn off because a float value inside of the skimmer would close down against the vacuum and isolate it. Once the pumps turn off, the float comes back up and the skimmer starts working again if there is enough water in the skimmer to keep the float up away from the vacuum. I remember that I could manually stick my hand to the bottom of the skimmer and push the float up and the vacuum would start pulling water through again. But I remember there was a tendency to have your hand pulled into the vacuum pipe if you were not careful...so safety wise I was probably doing something your not suppose to do.

My current pool does not have this at all.

Check your water level...the skimmer that is not working is not getting enough water or the vacuum on it is too strong relative to the other one.