OK - well I found a solution on this forum it seems like. I simply am pinging the Host computer after making the RDP connection and it seems to keep the connection open even if the screen goes to sleep.

If anyone has a more robust or better solution, please let me know. But at least I have a 100% stable connection (at least so far - it's been about 30 minutes since I've made the change and I haven't dropped the connection yet).

To do this I simply modified my script to read
(Subsituting my windows username and password, and the IP address of the host computer)

Edit - well the connection lasted over night on both my N770 and N800. So I claim success! Thanks to the members on this forum, because even though I found a solution before anyone replied. I found the solution by reading through some of the older threads.