There is a known issue with LCS 2003 and Windows Messenger being signed out overnight. The root cause is a known issue with fix for Kerberos. The KB article is still being published so not everyone knows about the issue.
You will want to enable the client side logging (RTCDLL) to report this issue and mention article 885887 (I am checking on the status of the article as it is not published yet).
To get a hotfix you have to open a support incident in order for us to track the customer and hotfix. You should get the call for free, but in the event you are charged that can be reversed just ask. Also not everyone has been trained on both LCS 2003 and 2005 so the first person you speak to may need to get some assistance, no big deal it will get to those who specialize as necessary.
Thanks John for asking the question prompting the post.
Toml LCS Kid