There are two sources for official UMC doctrine: The Articles of Faith of the Methodist Church, which are quite vague on the subject, and John Wesley's collected sermons.
In sermon XV, "The Lord Our Righteousness", he makes the following statement: "Even he that now standeth fast in the grace of God, in the faith that overcometh the world, may nevertheless fall into inward sin, and thereby 'make shipwreck of his faith'."
Wesley follows this with a later article he wrote on "Perseverance of the Saints", where he states more explicitly:
"Can any of these fall away? By
falling away, we mean, not barely falling into sin. This, it is granted, they may. But can they fall totally? Can any of these so fall from God as to perish everlastingly?
I am sensible either side of this question is attended with great difficulties, such as reason alone could never remove. Therefore "
to the law and to the testimony." Let the living oracles decide; and if these speak for us, we neither seek nor want farther witness.
On this authority, I believe a saint may fall away;
that one who is holy or righteous in the judgement of God himself may nevertheless so fall from God as to perish everlastingly." (
eternal security - Perseverance - John Wesley)