No.  The discount is given for payment up front and commitment to that term. Though you may cancel at any time, once you have canceled, you will have full use of your account until your premium term has expired. No full or prorated refunds will be given for cancellations prior to the end of your premium term under any circumstances.
 

If you are not sure you want to commit for a year or two, we recommend you sign up for a month at $9.95. If you are happy with the service you can always upgrade to a 1 or 2 year commitment at the discounted price and the unused portion of the $9.95 will be applied to your upgrade balance.
 

According to our terms of service (to which you agreed as a prerequisite of submitting your bank card), "ANY SERVICE FEES WILL BE CHARGED IN ADVANCE AND ARE NOT REFUNDABLE. If you cancel during the term in which you paid, the [FaxBetter] service for which you paid will continue through the term paid. NO PRORATED REFUNDS WILL BE GIVEN UNDER ANY CIRCUMSTANCES."
 

Many believe that you have 3 days after a sale to return any purchase regardless of the company's terms of service.  This is not true.  The Federal Trade Commission's 3-Day Cooling-Off Rule does NOT apply to the purchase of items sold online.