If your cmd.exe windows have "Quick edit" mode enabled, then if you (or somebody) left-clicks in the window (say to bring it to the top of the window stack), then it can select (highlight for copy & paste), one or more characters. A side effect of this is that output to the screen is suspended until the C&P is completed by right-clicking.

And if the program is regularly outputting to the screen, then undisplayed output will accumulate until the internal buffer fills, at which point the next write attempt will block until the select state is ended. Effectively suspending the program. The select state can be ended by right-clicking in the window so completing the copy & paste operation.

It can also be ended by typing any key, which abandons the C&P and allow the blocked write to succeed and the program to continue. Ie. Exactly the symptoms you've described.

The Quick-edit mode is very useful, but it can be confusing if you are not aware of it, or its affects.