I'm having trouble reliably getting a right-click menu to appear on PuTTY tabs, and then when it finally does appear it doesn't go away easily when I click elsewhere.
It's tricky to reproduce reliably, but you should be able to see it easily enough if you try the following just a couple of times:
Right click on an existing tab, choose to Duplicate it, type your credentials into the new tab that's just opened, and then immediately try to right click on that new Tab's header.
Most times, the right click menu won't appear and will take at least another one right-click (but sometimes more) before you can get it to display. Once it does appear, it seems to get stuck there: despite left-clicking somewhere else on the screen, or again on the actual tab itself, it is stubborn to disappear.
This is just one example of making this happen. Just generally clicking around and changing the focus from one tab to another, clicking inside the actual PuTTY windows, and then trying to right-click on the Tab header, you will no doubt notice that there are many instances where the expected menu does not appear.