The short answer for the "why" of the shortcut not working is, "I have no idea." The solution that often works to fix it, though, is either to edit the shortcut properties to remove the keyboard shortcut and re-add it afterward, or to nuke the desktop shortcut entirely, put a new one on the desktop, and reassign the shortcut you want to it.
As to turning off JAWS, what I'd suggest is that you don't. You have the option to put JAWS to sleep, but it is still running, until you wake it back up, or to turn off speech from JAWS, but keep all other aspects running, until you turn speech back on. But I'll be darned if I can find the commands for either in my own notes that I can dig up right now or in the Keystrokes document (and I would have sworn they were in that).
I think I've done both of these things with both JAWS and NVDA, but I could be getting confused, too.
Brian - Windows 10 Pro, 64-Bit, Version 2004, Build 19041
The purpose of education is not to validate ignorance but to overcome it.