It is not fair to keep a dog alone in an apartment all day, and definitely not if he is being kept in a crate. I think that if the occasional accident happens, it is only fair to put up with it – he is not being asked if he wants to go 9 hours without going to the toilet! IF he is a small dog you could consider litter-training him. Other than this, I would suggest you find a day-time pet sitter or a friend who can come round and walk your dog at lunchtime.