I seem to have fixed it...
I'm crossing my fingers that this will last, but so far so good. I was getting the internet connection starts but then stops problem described here. Sometimes, I couldn't even get a connection. Sometimes, if I left it alone and did nothing, the connection would suddenly reappear. I have a MBP running latest version of Parallels and I'm connecting to my DSL through a wireless router over the MBP's airport. Anyway, here's what I did...on a lark, I opened my Local Area Connection, and then opened the TCP/IP properties box. Instead of Obatin IP Address automatically, I clicked "use the following address" and just assigned it 192.168.1.106, an address that I knew was free. I set the subnet mask to the usual 255.255.255.0, and since my DSL router was located at 192.168.1.254, I put that in under default gateway. Then, since I don't much about any of this stuff, I also put 192.168.1.254 into the Perferred DNS server box and didn't put anything into the Alternate DNS server box. I clicked okay and tried it. Worked perfectly. I now get internet all the time, with no interruptions. In fact, I'm typing this over the connection right now. All the network info I used was taken from IPCONFIG/ALL, which I ran from command prompt in XP.