Harry's Patronus can't possibly work here. His "happy thought" is about facing death and destroying it rather than hiding from it; recall that he couldn't cast Patronus v1.0 because it required thinking happy thoughts about something else rather than facing death, and Harry couldn't do this. But the reason he's casting the spell is to convince himself that maybe there's a chance Hermione isn't dead after all, which is pretty much exactly the not-think-about-the-bad-thing mindset that didn't work for him then.

On the other hand, McGonagall is probably suffering from the typical problem of normal-Patronus casters: if your spell involves thinking about happy thoughts about something else other than death, then having evidence of death right in front of you is going to be a problem.

It's possible that the "lost some of the knack" thing implies that prolonged exposure to Harry Potter is wearing away at McGonagall's ability to think about something else. Of all the adult characters, McGonagall is probably the one most seriously thinking about Harry's ideas.