For me its their attitude.
If they come out saying 'Oi, no no no, not today pal!!' I take it worse than if they come out saying 'Oh, really sorry, but would you mind not doing them today'. Ive had that because the incontinent/senile/half-dead relative has come to convalese for a week and theyve only just got them to drop off in the guest room.
It would also depend on their reason, as Id ask; if they said 'Well, were going on holiday today' my response would be 'Im glad all my customers dont ask me not to do them when they go on holiday, otherwise Id have no income in the summer' they usually come round. Not always though.
Its as dissapointing as customers that sneak off without paying when youre halfway through doing their place that angers me.