Do I need a new prescription each time I place an order from ApriaDirect?

The short answer is no, you may use the same prescription on multiple orders if it is still valid. However, please consider the following:

In general, prescriptions are valid for 8 years, unless your doctor has written another expiration date for it.

A prescription written for a "Lifetime Need" or "99 Months" can be used to get the prescribed equipment as often as needed to continue therapy.
If a prescription notes a specific number of refills, the prescription will be valid to dispense the listed equipment the referenced number of times.
If a prescription notes an expiration date, it is valid through the listed date.