XP Pro Workstations lose connection to server overnight

I have a small office of 6 PC's all running XP Pro w/ SP1 (I am currently getting them all SP2). They call connect to a domain that is run on a Windows Server 2003 machine. We were on a domain that was run on a Windows Server 2000 machine until the last few weeks when we got a new server. However, for some reason, when we log on the next morning, we are unable to access the server. We can connect to the domain (or at least we can login to the domain) but we cannot access shares on the server. The software we use has its database on the server and it says "You do not have the permissions to access this network share." But when I try to access the folders (which we have as mapped network drives on each PC) it does not allow me to get in. After a reboot, this will fix the problem most of the time. Any clue what may be causing this and what to do to fix it? Thanks for your help.