Possible Causes

WARNING: This page is about a different car, the 2003 Mazda MPV and 2002 Mazda MPV. However, it is still accessible from the selected car via links, so may be relevant.

Immobilizer coil malfunction.
Immobilizer unit malfunction.
Key (transponder) malfunction.
Open or short between immobilizer unit and coil.
Open or short between immobilizer unit and PCM harness connectors.
PCM malfunction.