I don't regularly work from home, but I have solved several difficult problems while doing laundry, and I can specifically think of one time recently that was during a workday while I was folding towels. I know it's happened other times as well, I just can't specifically think if it was during the day while working from home.
I've also solved problems while showering, mowing the grass, eating dinner, and laying in bed trying to fall asleep.
Who knew -- developing software involves lots of thinking. You don't have to have your butt in a seat in front of the computer in the office to think. Sometimes doing something completely different is just what's necessary to break through -- whether this is getting up to get a drink, going for a walk, or doing sometimes completely non-computer-related like laundry.