Backup fails because of not enough room on destination sparseimage file???

[tubwreck]

My backup is failing because of an error copying a large (14GB) video clip file. The backup is being performed to a sparse disk image located on a network drive. Here are the attributes of the 3 volumes involved (pictures too):

Physical disk being backed up:
Capacity: 74.4 GB
Available: 15.59 GB
Used 58.81 GB

Network disk upon which the sparseimage file is located:
Capacity: 232.76 GB
Available: 134.14 GB
Used: 96.1 GB

Virtual disk opened from DMG file:
Capacity: 74.4 GB
Available: 14.53 GB
Used 59.87 GB

The copy fails partway through. I've gone in through the Finder and deleted the file, tried copying it manually, and tried the backup again. Nothing works.

I thought a sparseimage file would increase dynamically as required?

Thanks for any help,
Tubwreck ("Norrebo")