I'm sure some people set "run logon scripts syncronously" to make logon scripts run more reliably, I know our citrix supplier sets this on their sites and I've found that our logon scripts work 100% of the time with this set, without this set it seems they don't always work. I think in the past this has been due to very slow client PC's though but it's worth a try.
It's more likely to be that the drive is being remembered, do you use roaming profiles?
If you use a vb logon script you could add this section to clear all mapped drives before you map any new drives.
or this line to get rid of one line only
'Disconnect ALL mapped drives
Set clDrives = WshNetwork.EnumNetworkDrives
For i = 0 to clDrives.Count -1 Step 2
WSHNetwork.RemoveNetworkDrive clDrives.Item(i), True, True
'Disconnect any drive mappings as needed.
WSHNetwork.RemoveNetworkDrive "R:", True, True