I had a terrible time getting my Model S connected to WiFi myself, it probably took a week of experimentation. I tried 5 different routers and countless physical configurations (including router antenna orientations). In the process I discovered some silly things, such as the fact that extending or retracting the side-mirror affects your connectivity, indicating that it's probably changing the orientation of the car's antenna. I tried 3 different WiFi extenders. One of them was completely worthless, rebroadcasting on the same channel on which it receives. The first just didn't work well enough.
In the end, I found a configuration that works for me:
- Netgear Orbi mesh network, with at least one (Orbi) repeater within 30 ft of the car with no heavy obstructions (mine penetrates two outside walls, including a garage, but no heavy equipment)
- Kill all other wifi signals that you possibly can. Get a wifi scanner app for your phone, and make sure none of the signals it finds are yours except for the one you intend to keep.
In my case, my final network is the only one my car can see, the others are too weak for the car.
I don't recall whether I needed to tune the channels used, or whether the Orbi just took care of that. If you have a lot of neighbors, you might have more challenges than I.
Pay special attention to "xfinity" access points. If you use Comcast, and you see one in the air, it might be yours. You actually need to login to the xfinity website to configure your router to disable that feature--that's the only way to keep it from spamming valuable wifi channels. If you have neighbors, you might need to let them know about this, too.
In the end, the Orbi mesh network (with 2 repeaters) I wound up with is the most reliable wireless network I have ever used: it's not even close. I've only had to reboot it once in 4 months to force attachment after a firmware update, and I've never seen a client have problems connecting. I can't say these things about any other router I've ever connected to. But there's a good chance that this alone wouldn't have been enough for the car without eliminating the other signals. In my case, whereas it failed constantly before, my Model S connects with flawless consistency now.