I've seen this on a wide variety of hardware. At some point, perhaps prompted by connecting or disconnecting other devices (the mouse?), the touchpad stops responding. Only a reboot will fix it. It's as though it gets stuck in the middle of a transaction or something. No clue.
Update: I booted with the mouse plugged in, and never removed it. Just before doing so, I tested the touchpad, and it was dead. Maybe this is because I happened to boot up with the lid closed, as I was on external HDMI? I think it's safe to say at this point that this is easily reproduced within a workday. Locking and unlocking the screen a few times may be necessary. Perhaps there's a way to always make it happen, but I haven't had time to test it in a directed manner.
I confirmed that the mouse cursor can still be moved by using the touchscreen, and the keyboard still works, so this is definitely a touchpad issue. Plugging in an external mouse works fine too.