My DD played in plenty of downpours during her career ... and for some reason, it always seemed like it was coming down the hardest when she was pitching and not when her team was hitting! Anyhow, I told her from Day 1 that if it was raining hard, and the ball came back wet to her to ask for a new ball every pitch if she needed to. A couple of times they actually ended up stopping the game after she asked for a dry ball for about the 10th straight pitch, and a couple of times the rain let up before the inning was over probably helped by the fact that all the changes in and drying of the balls slowed down the inning.
At Eastern Nationals last year, we had a similar situation with the team we were coaching ... absolute downpour but great draining fields so the game kept going, but our pitcher was having a heck of a time getting a grip on the ball, so I called timeout to go out and talk to her to tell her to ask for a new ball every pitch if she needed to, to give her a towel to dry her hand off in between pitches, and honestly to buy a little time for the rain to pass. At one point, the umpire let everyone know that he was getting tired of all of the asking for new balls, and I let him know between innings that if it kept raining the hard and the ball was that wet, that she had every right to do it and that I didn't think our pitcher deserved any attitude from him about it. He actually apologized to me ... of course when we came up to bat, the rain had stopped.