First of all, Wifi has nothing to do with EDGE. So disabled EDGE from Airtel isnt going to help you at all.

Now, your Wifi problem. Are you anywhere close to the router?..
Because it seems like your Wifi connection is dropping due to low singal strenght.

When you connect to your Wifi network, do you put in the proper Password?
IE. What are you using WPA Password or WEP Passkey?