Found this thread because a similar thing just happened to me and I have several more data points for us all to ponder. I arrived at Target and plugged into the supercharger having 28% SOC. I immediately went into Target for some light shopping and looked at my app at least once to see how much time I had. When I saw 55 minutes, I realized that I hadn't reduced it back down to 80% after a long-distance trip I took last weekend, so I lowered it right then and there (in the app while standing in the store) from 100% to 80% bringing the remaining time down to 25 minutes... and thought nothing more of it. I finished shopping about 10 minutes later and upon returning to my car, noticed that charging had stopped at 45%. WTF? I looked at the plug (didn't touch it), got in the driver's seat to observe the screen and noticed that charging had just restarted. Cool... whatever... about 15 minutes later it reached 80% and stopped as expected. I left Target, did some more shopping at other stores, and upon opening my email when I got home I noticed an email from Tesla implying I was charged an idle fee for my recent supercharging session. It specifically stated that since this was my first charge for being idle, it would be waived and didn't state how long, nor how much I would have been charged otherwise. I called customer support expecting them to be able to tell me nothing about the incident and was saddened that I was 100% correct. They said I should have received a notification on my phone that charging had stopped but there was none. There WAS a notification from when my car completed its charge YESTERDAY, but nothing from today... from either of the two times it stopped charging TODAY.
The email basically threatened me to add a payment method to my account or risk losing supercharging (ok, not in so many words, but I'm a little pissed right now).
Before I started this diatribe I had forgotten the whole 100%-80% thing I did in the store, but writing this all down reminded me of that fact, and I now wonder if charging stops when you change the charging limit via the app when it's already charging. I'll be testing this next time, but if anybody has any experience in this regard, it could save me the time and maybe help others out too. I'll report back what I find when I do, and suppose I should add that credit card to my app so I don't lose the ability to supercharge.
Thanks for reading!