We have 2003 SP1 and 2003 R2 (SP1 implied) boxes that I keep patched monthly, and I haven't seen this issue. As a workaround, could you run a script nightly that restart the Terminal Services service?

I connect to my PC at home using the Remote Desktop Web Connection & occasionally I need to be able to re-boot it remotely. I know I have seen scripts to re-boot an XP box, but for the life of me I ...

If remote desktop can’t connect to the remote computer and fails with the error message Your computer could not connect to another console session on your Windows ...