Does the Methodist Protestant Church believe in the doctrine known as “once saved always saved?”

No. When you enter a relationship with Christ, often called getting saved, you still have the ability to choose if you will continue to live for God. You are able to live a consistent life of service to and love for God by the power of the Holy Spirit working in your life. The Bible teaches in 1 John 2 that God’s purpose for you is that you do not sin. However, John also states that if you do sin, then Jesus is your advocate. In 1 John 1 you are taught to “walk in the light” of God’s love. However, you are warned in Ezekiel 18 about the dangers of sin, which states in verse twenty “The soul that sins is the soul that dies.”
God’s purpose for you is to live consistently following the example of Christ as John teaches in 1 John 2. The Bible also teaches that God does not desire that anyone should perish but that everyone should come to repentance (2 Peter 3:9). Therefore Jesus died that everyone who believes in Him will be saved (John 3:15).