No. Think of it as a hard drive that has run out of space. You can re-use the space as often as you like by deleting files that you no longer need online (that the intended recipient has already downloaded).
If you need more storage, e.g. to send larger files, then you would need to upgrade to a larger storage plan. Each of our plans offers incremental storage upgrades without having to upgrade to a larger base plan. Like new orders, upgrade orders are guaranteed to be provisioned within 30 minutes, often much quicker.
Note - existing customers prior to June 1, 2008 may have plans that have both a soft storage limit and a hard storage limit. The hard limit is 120% of the soft limit. In that case, these customers can exceed their soft limit by up to 20%, but the hard limit works just like our the storage limit as described above.