So I just ran into a very similar issue on our new laptop and it might be the reason for the trouble here...

On our new laptop, the touchpad is very wide and sensitive. When I have it enabled and am typing, I kept accidentally tap clicking which was incredibly annoying. In order to prevent this, I set it so that the computer automatically disables clicking while it senses typing.

And just now I was wondering why my mouse was taking 2-3 clicks to register when I was just filling in some data in the database and it was because of this setting.

So far, all of the complaints about this issue are with laptops or tablets. Most newer devices now a days probably have this enabled by default. When using the battle system, if you're pressing hotkeys, the device thinks you're typing and therefore will disable button presses for about a second or two after each key press.

Is it possible this is the issue you guys are experiencing?

Unfortunately, there's nothing I can do on my end about this issue. You will either have to disable the feature, not use hotkeys, or just expect the 1-2 second delay.

OMG! I turned it off and that worked!