Both of my kids were like this. One still sometimes needs reminders even at 4.5 when he is playing something he really likes. I can see him squirming but he'll insist he doesn't need to go. They don't want to stop what they're doing to go to the bathroom. Honestly I think I even remember having an accident or two at K (I started at 4, back in the day when the cutoff was later) because I put it off as long as I could until I couldn't hold it anymore. It's frustrating because they are the only ones who can feel the urge to go and they have to want to get to the bathroom in time. I think if nothing else it eventually works itself out when they become more socially aware and don't want others to see they have had an accident.