Earlier this year, I received a paper to referee for the top journal in my field of research. I know both of the authors. The first recently completed a Ph.D. working with a friend of mine. My faculty friend is the best-known person working in our area; he is an extremely careful and conscientious researcher, and working under him, the student produced some very good work. The other author of the manuscript I'm refereeing is the new post-doctoral supervisor of that recent Ph.D. grad. He is a very senior but not terribly distinguished scientist, and I think that some of his work is rather slipshod.
The first manuscript draft I got from this pair of authors had a glaring problem. There may have been a fundamental error in how they interpreted their results. There are two different ways that the system they are studying could behave, and they assume that it goes one way, apparently without even noticing the other. They might well be right about how the system behaves, but I sent back a report saying that the work would be publishable if they either explained why they only considered one of the two possibilities or expanded their analysis to cover both. The final conclusion is likely to unchanged whichever way the system behaves, but it is important to verify this; moreover, it is interesting in its own right to know which way things go.
After a rather brief period, I got a revised manuscript back from the journal. The authors had made a number of other minor corrections that I asked for, but they basically ignored my main point. At this point, I'm not sure what to do. I still feel like the paper contains a significant amount of interesting material, and it could be fixed without that much effort. However, I am upset that the authors made not effort to fix the actual problem I pointed out. They don't even really acknowledge the problem in their resubmission letter.
I was the only referee who turned in a report on the first draft, so what I say will almost certainly determine whether the paper is published. Should I send it back one more time, insisting that the changes I called for actually be made this time? Or should I recommend rejection, since the authors are apparently unwilling to make reasonable adjustments.