He refuses if they are not
Your heels are your basis to solidity in your tack - if you do not have a strong and developed, balanced seat.
Your heels not only anchor you, but also aids your inner calf to do its job - which is to remain solid and supportive around your horses girth.
I find, that when I loose my heels, I loose my supportiveness around my horses girth, which then causes him to feel "abandoned" I guess you could say - and he stops. Like saying "woah, where'd you go? If you aren't going over, neither am I"
Also, when you don't use your anchor, a domino effect occurs in your body - which results in losing your seat, and etc, etc.
It's hard to say what exactly goes on when you loose your heels without seeing a vid, but my guess is what I've stated - you lost your inner calf, your lower leg results and etc, etc - which then creates the refusal because you've abandoned your horse at the base of the fence.
Not all horses require that, many just do their jobs regardless of rider error - which helps and doesn't help their rider at the same time.
I cherrish those horses who don't continue to do their jobs due to rider error, because those horses, are truely teaching us to become more effective, correct riders.