Do Catholics subscribe to the "once saved, always saved" doctrine that many evangelical Christians believe in?

Many evangelical Christians say that once a person has accepted Jesus as their Savior and repented of their sins they have formed a bond between their soul and the Lord that is unbreakable. Do Catholics believe that this is true? I have heard that confession of sins to a Priest is common in Catholicism, and wondered how a Catholic would respond to a once saved always saved Christian.