First off, you won't be able to get tickets for new services.

What happens to the Kerberized services that you are using depends on how
they are implemented.

All implementations of telnetd, rlogind, and other remote login utilities
generally only check the ticket expiration time at login time, and don't
care about it afterwards. However, AFS will not give you access to your
files anymore, even if you already have files open.

Note, however, that this is just a matter of implementation. Someone could
write a version of telnetd that closed your connection when your ticket
expired, but I doubt that it would be very popular :-)