Coms and visibility, especially IR and sonar based, the moisture in the air can cause havoc with those as well as shortening the Mk1 eyeball as well.
British forces would be less effected by it than anyone else, as justified by Slims statement that the British army fights all its battle on the side of a hill, in the pouring rain and on the join of 2 maps.
If you are talking very heavy rain, entrenchments become a pain, digging mud is horrible and feels like an endless task. Standing in them is even worse. So anything below the water table is specialist build. Any defences are more likely the Ypre raised breastwork than the set into the ground type.