Performing prayers and covering the hair, they are both orders of Allah. When you are performing a prayer, you are following an order that came from Allah; so just like it, you should observe hijab and obey Him in this subject, too.
Not fulfilling one obligation does not invalidate the other one that you fulfilled, though. If you established your prayer, you fulfilled a commandment from Him. Exposing your hair out of prayers does not invalidate your prayer; also it does not break or harm your ablution (wudu).
Wudu-breakers are listed in the following fatwa: