Is a man still qualified to be an elder after the death of his wife?
If you asked one hundred elders or preachers whether an elder should continue as such after his wife died, you would probably get fifty who say yes and fifty who say no. At least a third of those might even say an elder is an elder for life unless he resigns, moves, or is removed for cause. I personally believe that it is up to the congregation involved to make that decision.
My own view on the matter is that the man is qualified to continue as an elder. The passage in 1 Timothy 3:2 says “an overseer then must be blameless, the husband of one wife, vigilant, sober, of good behavior, a lover of strangers, able to teach.” What is commonly translated “the husband of one wife” is literally “a one woman man,” although the terms often refer to husband and wife. The idea is that he splits his loyalties in marriage then he is likely to do so in spiritual matters. The death of the “one woman” would not change that. Perhaps he should resign because of his grief and the reduction in his ability to act as an elder (because a wife is of much value to an elder), but I don’t think he should be required to resign.
But then, many would disagree with me on the issue of the meaning of “husband of one wife.” For instance, I believe that a widower who marries someone else is still qualified to be an elder because he is still the husband of one wife. I believe that a properly divorced man who has married another is qualified under this requirement.
A companion question to yours would be whether a man who has been an elder and then has a child later in life is still qualified. Or, if an elder has two believing children and one later rejects Christianity, does that disqualify him. Those who say that all of an elder’s children have to be believers would say he has to resign. Those that say that any one of an elder’s children must be a believer would say he could continue.
A similar question arises. If this elder is one of only two in the congregation, and he is required to resign, then does the one remaining elder have to resign or can a congregation have one elder? Should a man be forced to resign because of someone else’s disqualification?
It is complex questions like these, including yours, that make me believe that each congregation should decide such difficult questions for themselves. After all, that is what the elders are for. They should be deciding these questions rather than what color carpet to put in or how many songs to sing on Sunday morning.