Domain transfer question

[bodsham]

I have been trying to transfer a domain out of Bluehost for two weeks. It requires a code. They tell me by email it has been sent. It never arrives. They say sometimes these codes get stopped by spam checkers. I have taken off all the spam checkers on two different email addresses and still the code doesn't arrive. I have changed the admin address for the account as they suggested. Still it doesn't turn up.
Bluehost now no longer respond to my inquiries about how I can transfer this domain away from them. Is this typical? Is there anything to stop them effectively shutting down this site name because I am cancelling my hosting with them?