You register the domain name in your own name, and unless there is some legal reason why, the registrar cannot refuse to renew you, and also cannot charge you a higher price than what is advertised as a renewal rate.
If by some strange chance something like that WOULD occur, you are always free to transfer your domain to another registrar instead of renewing with the same one, so as long as you initiate the transfer before the expiration date, there will be no hassles with that, and since hosting is a separate issue, transferring a domain name will not affect your site.
The most important thing you can do for your own protection is to be sure to use a valid email on your domain registration, and KEEP IT UP TO DATE. if you change email addresses, your registrar will never be able to reach you to notify you of expiration dates and any other important information you may need. Your Admin Contact email is your domain lifeline! I see more lost domains because of outdated contact information and no way to verify a domain's real owner than I'd like to say. Save yourself the worry and stay up to date. 
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