yes, the net connection is completely provided by WinUAE. There's no TCP/IP protocol installed in AmiKit.
When Amiga side reports there's no connection and you immediately switch to Windows, are you able to connect there?
I am using WinUAE 1.3.2 and I haven't experienced such a problem. However I don't use wi-fi with WinUAE very often.
Anyway, the latest version of WinUAE is 1.3.4. You might want to try it because the history log says: "Improved bsdsocket emulation stability"
- that's the feature that provides the connectivity for the Amiga side.
Just read the following thread
before installing WinUAE 1.3.4. It contains a path bug, which might prevent AmiKit from running.