I’m talking about the following specific scenario.
Poster A opens a thread asking why colorless green dreams sleep furiously, which drops like a rock.
Next day Poster A bumps the thread.
On the third day, is it OK if Poster B comes along and bumps it again, saying, “I’ve always wondered why colorless green dreams sleep furiously, but I don’t know the answer either.”
I know the underlying principle is that if a thread sinks, it means that nobody’s interested in it and it shouldn’t be bumped; yet, Poster B’s reply indicates that other people probably are interested in the question, and the thread should be allowed to live.
What do the moderators and other members think?
i do that all the time.
bump card - go directly to top of page, do not pass the stickies, do not feed the hamsters.
I think that colorless green ideas sleep furiously. 
But I also think that your scenario is ok – personally, I don’t care how many times a thread gets bumped, it’s more the timeframe. Especially since threads can disappear off the first page of any given forum pretty quickly around here. Bump away, I say, but if no one has responded after, oh, a week (?), let the thread die a natural, peaceful death.
But that’s just my $0.02. 
Well… I suppose that would be OK, up to a point. But poster B only gets to do that once. If we have sixteen posters bumping a thread and no one answering, the it becomes clear that no one knows (or no one wants to be bothered) and the thing needs to disappear into the depths and stay there.