Madhav,

If the tape drive is shared you should be able to write the backup to the other Server's device providing the account running the SQL Agent has rights to that device.

A different suggestion would be to backup the Database to disk and then copy that backup to tape, assuming that you have adequate space to do. In my mind this does a couple things a) It helps with redundancy, even if it is for a very short term b) recovering from disk is faster than from tape (although the difference may be negligible with 1.4 TB Database)

You might even try backing up the Database to disk as a troubleshooting step. Maybe there is some other activity occurring on the Server during the backup that is causing the issue.

Food for thought!