Yes, that is the problem.

In most cases prompted will probably work most of the time.  If the TSM
client and server are in contact frequently enough that the client doesn't
lose it's DHCP lease for the current IP address, there should be no problem.
I think DHCP generally lets a client keep the same lease a long time, as
long as the IP address is in use.  Or, if the client is a desktop that is
booted daily, the client scheduler will contact the server with its new IP
address as it comes up.  I think the problem would probably be if you had
activity with the client scheduled infrequently, like on weekends only, so
there is a good chance the IP address could change since the last contact.

If you do lose your IP lease, it is a pain and requires manual intervention.
So we use POLLIING by default.  I don't know of any disadvantage to using
POLLING if all you are doing is backups; you just can't force new schedules
down from the server immediately.

Maybe someone else who uses PROMPTED a lot can speak to how they manage in a
DHCP environment.