Always, always control your own domain registration and do so at a reputable registrar. Don't use your webhost and don't use a company that does anything but domain services.
Companies that do registration on the side or as a bonus to hosting packages tend to do things like automatically re-register your domain even after billing fails without notifying you, then submit the whole $20 to a bill collector without notifying you, keep the domain operating for an extra 6 months so you have no idea that anything went wrong, but kill it after said 6 months with another 6 months left on the registration with no way to make any changes to the domain because they refer any support requests to the bill collector -- because this definitely did not happen to me and it definitely didn't happen at a company called 1&1 Internet Inc. because that would be totally absurd. cough.