If a minister's wife leaves him, is it still biblical for him to stay in the pulpit? She left him as she didn't want to be a preacher's wife any longer. He preaches for a church of Christ.
There are few qualifications on a preacher, beyond his ability to do his job. A preacher can be unmarried as Paul and Barnabas were, or if he is married, his wife is to be a believer. "Do we not have a right to take along a believing wife, even as the rest of the apostles and the brothers of the Lord and Cephas?" (I Corinthians 9:5).
Since his wife left him because of his job, neither he nor she have the right to marry another person. "But to the married I give instructions, not I, but the Lord, that the wife should not leave her husband (but if she does leave, she must remain unmarried, or else be reconciled to her husband), and that the husband should not divorce his wife" (I Corinthians 7:10-11). However, given what you presented, I don't see anything that would disqualify a man from preaching the gospel.
Whether the local church wishes to continue financially supporting this man is something only the local brethren there can decide.