I've been having similar problems. My iPhone app has not been reliably connecting for about 2 weeks now.
I've got the latest version (3.8.6), and now that you mention it, the problems started around when I downloaded that update.
Earlier this week, I was at a supercharger and couldn't log in to see how much juice I had. Last night, I tried to summon, but the app would never connect. The phone lets me open the door and drive, but not always connect when I'm outside the car.
I've called Tesla twice about this. The first time, they pushed an update to my car, and it seemed to help for a few days, but then the issue returned. I called them again while I was supercharging, but the guy on the phone offered no advice other than the things I'd already done (shut down the phone, log in and out of the app, delete and re-download the app).
I’ve also had more connectivity issues since the last update than I had in 6 months prior to it. I’m hoping the next round of updates will address the issues. One time this week I had to get in my car without pre-cooling it, it was a reminder of the dark ages when cars weren’t perfectly 70deg when you get in even though its 103 outside!