While I do think the manager bears the vast majority of the responsibility in situations like these, the reality is that you're right, and oftentimes managers do a bad job because they're getting pressured from above to communicate and don't know what to do.
You can often get them on your side by giving them a plan that makes them feel like they're in control (again, totally not your responsibility! But better than dealing with them being obnoxious constantly). If they ask for an update and you say, "I don't know what's wrong, but we're looking into it" then they don't know what to do. If you tell them "I don't know what's wrong, but right now we're investigating x because we suspect that's the source of the issue. I'm checking the logs and other engineer is trying to recreate the issue in a clean environment. Unfortunately I don't have a good answer as to how long it'll take, but we'll update you either when we've learned something useful or in two hours, whichever is sooner," then they have something to say to the people above them and they understand when they'll get an update, so they don't need to bother you.
A helpless manager is like a child - if left alone, they'll just shout and cause problems. What they really need is direction and structure.