My sprinkler head pools a good amount of water only while it is running. Looking online, I can only find reference to low head drainage, which I don't think this is since it doesn't pool once that zone is turned off. Is this most likely a broken head that just needs to be replaced?
If it is a "pop-up" type , there is something like a rubber "O" ring it pushes through. These rings leak , it is a matter of how much. As they get old the rubber is more likely to leak. The rubber is not difficult to replace except the manufactures seem to change something every year so finding an exact replacement is likely to be a problem .Replacement of the head is likely the easiest, fastest thing to do. Replacement also covers the chance that it is a different problem. I had a couple heads leak last year, I thought it was O rings but when I examined them , the bodies were cracked by freezing . The cracks only opened to be visible when under pressure.
If it is one of many sprinkler heads compare the throw distance (the distance the water travels from the head at max distance) to the other heads. If there is a significant difference then a greater volume of water will be dumped around the head than the system plans for. Check that the jet is not unnecessarily obstructed.