I have dropped one account before over messy dog yards and I'm about to do the same with another. I get tired of getting it all over the mower and sometimes I'll get into a pile that makes me gag...light colored and sticky and smelly as all hell.
One tip...keep your mouth closed when trimming and carry a spare shirt!
I just recalled that I dropped one other but that was after the first mow. I talked to the lady about it and she said that they never pick up the dog crap and probably never will. She won't, the kids won't and the husband can't really (wheel chair).