Kerberos Ticket Renewal Problem with SC Logon

Hi,
I'm experiencing problems whereby users (who've logged on with smart
cards) leave their machines logged on overnight. On unlocking their
workstations in the morning users get a message in their system tray
telling them that Windows needs their current credentials and a green
Kerberos icon in the systray. The users try to renew their credentials
as instructed by locking / unlocking their workstation, but alas no
success. The users cannot shutdown gracefully as their connections to
their network shares are dropped which stops them saving their profile.

I think this is due to the Kerberos user ticket expiring after the
default 10 hours? Shouldn't Kerberos re-authenticate silently in the
background after unlocking the workstation in the morning. I know that
the users should log off, but they don't and this cannot be changed!

Any ideas?

.