Way ahead of you. I tried a neighbor (same ISP) and it failed in the same way BUT it seemed to work at first when parked in their driveway (some distance from the router), but failed a few minutes later.
I was clutching at straws. I know another friend whose car does connect correctly (a new Model 3 with HW3). I need to go over there (but it's 40 miles away). I guess I need to make a housecall.
Are you connecting on 2.4Ghz or 5.0Ghz WIFI?
I always split mine to be on separate SSID so I can control what each device connects to. Some applications are better for one vs the other.
5.0 Ghz has higher bandwidth and less interference. 2.4Ghz has longer reach.
I also run apps (wifi scanners) on my phone to find the least busy channels for 2.4Ghz rather than let Router pick channels dynamically for you.
Also setting channels too wide, fixed or dynamically, (for more bandwidth) can be more subject to failure and interference.
Reliable slow connections are often better than fast unstable ones.
On better routers you can go in and look at the logs see why it's dropping.