If I register my valuable domain names with whois privacy protection and my registrar goes bust(it is a small player) is there any danger I may lose the domain name somehow?

Yup. One didn't exactly go bankrupt but went bust anyway, look up the Registerfly fiasco.

malcarada, if your company is ICANN accredited I don't think you have much to worry about.

Registerfly never should of been a fiasco. ICANN and everyone else seen that derailment coming way before it happened. ICANN just acted like a government bureaucracy handling it.