On the verge of losing his job, a young record executive is assigned the task of reuniting a group of middle-aged losers, who formerly comprised an infamous, long-forgotten boy band.

I agree with the previous comment.
McKee ('story') suggests to alternate positives and negatives to build interest, there's maybe too negatives in you logline: losing his job (-), middle age loser (-), infamous, long-forgotten boy band (-).
Changing the last element to "hugely popular boy band" (+) works better.

I guess, my first thought would be, if the boy band is long-forgotten, why is anyone in the record industry looking to reunite them.

You are better off with a hugely popular boy band who have vowed never to play again. Now the exec must get them to put aside all their old arguments and reunite or lose his job.