Have you looked at the slide valve in the bottom of the skimmer? Most have a little cover that slides back and forth to change the suction level.
Second would be, do you know how the piping is run? Are all skimmers/drains home run back to the equipment pad or are they daisy chained on the same pipe? If they are all on one pipe, this is where those little valves on the bottom of the skimmer come into play so you can adjust the flow.
A third possibility is that something fell down that pipe when the skimmer basket was out. One of my skimmer pipes had a large rock (egg sized river rock) down the pipe. I could see it down at the bottom, apparently (lucky for me) it was too large to make the turn in the pipe so with a bent coat hanger I was able to get it out.