I have a suggestion that basically involves using k5start from Russ Albury which I suspect will no longer be as maintained in the future. Available at http://www.eyrie.org/~eagle/software/kstart/k5start.html and having that maintain credentials in the session, then copying the KRB5CCNAME into a new session and having it renew the Kerberos tickets, so when k5start runs aklog it'll renew the tokens in the suspended session. It's not ideal but it does allow you to have session resuming.

I am not sure what the security implications would be doing this since I suspect this would be frowned on by the Kerberos community. This k5start tool was intended to keep long running processes from losing their file system access on a host.