Hello and welcome to Apple Support Communities kendon192,
I see that you're losing internet connection when you have your MacBook Air connected to your TV for a display. I can understand your concern with this, and I'd be happy to look into this with you.
I know that you asked about using a different adapter, and you certainly can try one. However, there are some troubleshooting steps we can work through which can help you begin to isolate the issue further. You could be dealing with some wireless or Bluetooth interference. The article below provides some more details and some steps that can help.
Resolve Wi-Fi and Bluetooth issues caused by wireless interference
Let me know how this goes and if you see any changes.
Have a great day!