one thing i found with networking and Zone Alarm is that you need to set ZA to allow ics,
i use ZA Pro so i apologise if it is different.
double click the ZA icon next to the clock, click the firewall tab
click advanced near the botom right, in the Internet Connection Sharing section, click so the "this computer is an ICS/NAT gateway and in the box underneath, choose the IP address of your desktop network connection (192.168.0.1) for example (you can find this by opening network connections, right click the network connection, choose Status, then support.
close the za box and your system hopefully will not keep dropping the network.
restart your desktop and check if it has worked, Fingers crossed.