I had the same problem, so I contacted my host's Help Desk. Their reply was:
"Your scripts are attempting to use more than php's default memory limit for scripts. Accounts on our shared servers are not allowed to use an excessive amount of system resources. If your scripts need to use more than what is currently available, you should either try optimizing your scripts and databases or look for a dedicated server."
They doubled the limit temporarily, which allowed me to restore my database. It runs fine now.
Hope this helps.
Oz.