I tested just now, and I wasn't able to replicate it. The feeder should be able to feed regardless of what the milker is doing. Are you able to post a gif or a screenshot of what's happening?
Edit: could it be that the cowgirl is maxed out on nutrition? If the cowgirl has something like 10k nutrition, she will stop consuming food, so it will stay in her inventory and the feeder won't be able to give her anything more.