I don't see how you could have the same error messages if you switched to pointing at the volumes, rather than the image files - and you can't check "On successful completion" in a scheduled copy, because you're not looking at the schedule...

here is what I did. I will repeat everything one more time to see if it makes a difference this time.
In Finder I opened the sparse image file so that "idisk daily backup" is listed under DEVICES.
I deleted the old scheduled backup for idisk dailybackup and created a new one scheduling it every night with the option to eject idisk daily backup "on successful completion".
I ran copy which it did successfully.
I then ran the weekly and monthly backups successfully as well since they usually run if another of the sparse image files was opened previously, probably because Finder is still showing their sparse image files. I did not change their option to eject because their sparse image volume wasn't listed on the choices of what I could eject "on successful completion.

rebooted
Tried to run idisk daily backup from scheduled copies and got same "failed to boot idisk daily backup" preceded with the same error message; "there was a problem connecting to the server"cindy's time capsule the share does not exist……."

I have the same problem on my mbp but that backup takes over 30 minutes so it is not as easy to test and retest quickly. But that is the backup I really care about since I take that computer back and forth every day and sometimes forget to plugin the external drive or to access the sparse image before I go to sleep.

I'm afraid I don't have any other suggestions. Since the OS seems to be unable to remount the share, it's hard for us to proceed with the backup.

Perhaps you can set up a login item to mount the share when you log in?

login item doesn't work. Time capsule and ext disk name are greyed out. It allows me to add the sparse image but when I restart I get the same "there was a problem connecting to the server"cindy's time capsule the share does not exist……." and the kind listed in the login items list changes to unknown.
ANy other ideas? I tried the Automater route as a calendar item to open every night at midnight, but that didn't work. I will try to see if there was something wrong with my Automater instructions.

It's curious that both Apple's own code and our attempt to mount the Time Capsule don't work, Cindy - that confirms that this seems to be an Apple problem.

Do you have a password set for the share?

No I do not have a password.

I have been waiting for some help from the apple discussions list however there have been 0 replies after 68 views so far to my question.
And I have been trying to get Automator to work for me to handle this but I've had no luck so far.

I have written a simple automator workflow to open the sparse image file. It works when I first create it and run it within automator but fails if I save it as an ical event, or save it as an application and run it later, or even if I save it as a workflow and run it with Automator runner. Actually the only time it works is when I first create the workflow. It even fails if I keep the same workflow in Automator open and try to run the next night. I think just setting up the "Get specified Finder items" works and so when I first run it I get a successful run but not the next day. All other times the sparse image is not loaded into DEVICES and when I try to run the SuperDuper backup I get that same blasted error message:

"There was a problem connecting to the server"…....'s Time capsule". The share does not exist on the server. Please check the share name, and then try again."

So I am unable to find any help with Automator and don't know anything about Apple Script so I guess I have to give up.

THank you for your help. I may try to call Apple and get help but I am not very optimistic about that happening either.