Hi Marie,
I have been having the exact same issue with my Toshiba Satellite S75t for a couple of years. I never knew what was causing it and in spite of trying all kinds of troubleshooting (reinstalling drivers, running various DSIM commands etc.) I could never fix it on demand and would just go back to using an external mouse until the touchpad functionality would magically return after some period of time. However I recently started seeing a pattern. I believe the issue has something to do with the incoming voltage to the laptop. (I'm NOT an electrical engineer so this is just a guess!)
I would normally have the laptop plugged into a power strip. One time when the touchpad was inoperable, I plugged the laptop directly into a wall outlet for some unknown reason and rebooted, I noticed that the touchpad was working again shortly after. Then at another time when I noticed I'd lost the touchpad again, I checked the power supply and found that the plug was pulled partially out of the wall socket. It was still getting power, because the battery wasn't draining but apparently there was something wonky about the incoming power supply. After I plugged it in completely and rebooted, I got the touchpad back again.
The last time I lost the touchpad, the laptop was securely plugged into the wall and rebooting didn't help. So I tried the following steps and managed to get the touchpad back again:
1. Shut the laptop down completely
2. Remove the battery and unplug the laptop
3. Press and hold power button for about 30 seconds (not sure if this is necessary)
4. Plug laptop back in (directly into a wall socket) but leave the battery out
5. Press power button to turn the laptop back on
6. When the Toshiba screen first shows up, press and hold power button again until laptop shuts down again (again, not sure if this is necessary. I just wanted to make sure it was completely shut down so it would cold boot)
7. Press again to start up (with the battery still out)
8. Allow it to boot up completely
9. Check Mouse setting (under Control Panel), or check Device Manager or run Function app to make sure touchpad is recognized again
10. After the system is fully booted up, put the battery back in and carry on!
Long story short, I'm thinking it may be some kind of glitch in how the touchpad is receiving power and when you run through this process to "reset" everything from an electrical standpoint, it comes back. It's worth a shot anyway. You definitely have my sympathy on this. The struggle is real!
Good luck!