We've found TT both our boys to be fantastic one day and loads of accidents the next. Neither of ours got it within a few days and the eldest is still in night pull ups.
I've found that when asking our 2.5 yr old, he will often say no, he doesn't need to go wee, only to find he's wet his pants 2 mins later. It's like putting the thought out there and then he needs to go. I've found prompting him and getting him to sit on the toilet at regular intervals far more successful, than asking his opinion or waiting for him to iniate it himself - that comes later. Also, we did it over the summer holidays when we were home and didn't have any commitments planned. We also found with DS2 that the 'novelty' of using the toilet went after a few months and he started refusing to go. We're still struggling to get number 2's happening on the toilet, but wees have improved. So, yes, we've had more than 8 accidents in a day. They do eventually get it.