Actually there is a front wiper system relay so inspecting that would be essential. I like to start at the working device, which is the wiper motor, and make sure that I am getting power and ground when the switch is energized. If I am then you have pretty confirmed that the wiper motor is the problem, if not, then you trace back through the system.
Have you contacted Mazda, to see if there is any warranty extension? I checked for Technical Service Bulletins, but don't see anything yet.
Here is a web site that has very good repair info for your car, including a wiper system wiring diagram.
http://bit.ly/mitchell_repair_manuals_online
Hope that this helps!