I have an older Samsung S5 running Version 5 Android (Lollipop), so those options aren't avail. Read on if you want to know how I fixed mine (I hope/think). Post Update... still testing, I think I need to enable Location Services as well (battery drain) to allow it to work at home all the time... I'll update this when I know I've got it right. Post-post update - I'm going to Service. Now it doesn't stay connected unless I go into Bluetooth settings and re-connect every time. I think I'm close (believe it or not) and stuff below may still apply.
I did a Google search on "Using Trusted Devices to Unlock Your Phone". When you dig in you'll find that you need to set up Smart Lock but I couldn't find anything to set Tesla device as "Trusted." That's because I was only requiring "Swipe" to unlock my phone, so security wouldn't allow Google Smart Lock.
When I applied a pattern to unlock my screen, then went to Settings - Security - Smart Lock (FYI, same screen - Trusted Agents is where you turn it on Smart Lock), then it will ask for your swipe pattern (or code I assume if that's how you set your phone security). Then press Trusted Devices. I found Tesla listed already, but there's an option to add a device. So far so good, phone still in pocket and my M3 unlocks just fine.
FYI, Tesla did tell me to set this months ago, but they had no idea how (and neither did I because it wasn't available without first enabling Smart Lock). I plan to update Tesla Service now - this is too important to not understand!!! Someone buy them a few versions of Android and include it in their testing - please! They could avoid having to create Key FOBs as once tweeted by Elon.
I'm on the right track... after removing the phone association in the car and reinstalling the app (as required to re-establish the link). Not sure why it hosed up, but I followed the same things above, got to that good point and it works again. Car opening at home, never having to pull it out of my pocket.
Hope this helps someone out there... Basically, the problem was that I was using a swipe only to unlock my phone.