A lot of people are getting disconnected from Diablo 3 with Error 3007. One of the fixes listed on the forums seems to be sending a message to Global Chat every few seconds / minutes. So, since a buddy of mine was experiencing exactly this issue, I wrote a script which will do this automatically for him. The first time he used it he ran for 1.5 hours with no disconnects. He turned off the script and was dropped at the 3 minute mark. Logged back in and was dropped after 5 minutes. Ran the script again and had no more drops. So, anecdotally, it works. However your mileage may vary.
Leave a comment here if you have any questions / comments / concerns. Or feel free to buy me a beer if this script finally lets you play D3 :)