I think the problem is the USB port on the Slate does not pass sufficient voltage for a tethered phone to maintain a charge. I did some checking using two USB volt meters. One from Klein on the input to the Slate: USB Digital Meter, USB-A and USB-C - ET920 | Klein Tools - For Professionals since 1857
Then another in-line between the Slate and a Samsung S8 phone being used for cell data tethering via USB. This one passes both voltage AND allows tethering: https://www.amazon.com/gp/product/B07DCSNHNB
This one, unfortunately does NOT allow tethering (so don’t get it): https://www.amazon.com/gp/product/B07JYVPLLJ/
My discovery was that the Slate does not pass the full voltage to the USB port. It varied a bit, but even with between 5.04 to 5.17 vdc into the Slate, the USB output was only between 4.5 and 4.6 vdc with the phone tethered (at .155 amps). I think this lower voltage prevents the phone from charging itself effectively. Thus the battery runs down while it’s tethering and eventually the phone dies.
I also have a B1300 and that does a better job of passing voltage. From it’s 12vdc wall adapter it would pass 5.03 vdc without a load, and 4.88 with a .85A load (the phone tethered and at a 5% charge).
I did not try it with other phones. I’ve previously used a Google Pixel for this, but that had other problems with being unable to be defaulted to keeping the tethered state active.
I don’t know if this means my Slate is ‘defective’ or if the design of the voltage regulator in it isn’t up to the task of keeping an actively tethered S8 phone charged.