Wireless Network Adapters communicate with a Wireless Router using 802.11g (or similar) wireless networking protocol. This has nothing to do with ADSL, which is the technology by which the ADSL Modem transfers the broadband service over the phone line.
If you are experiencing dropped wireless connections, there are a couple of things you can try:
1) In the router's wireless settings, change the Channel number used for the radio transmission. This might overcome interference problems, which cause connections to drop.
2) In the Wireless Network Adapter's TCP/IP Properties, give it a fixed IP address. This eliminates the problem of the adapter failing to regain its IP address if the connection is lost briefly.