A low speed stall when the throttle pedal is slightly pressed and released may mean the Engine Control Module (ECM) needs to be reflashed (updated).Google+
Car Problem Reports
Mazda Mazda3 Engine Stalling at Lower Speeds
Mazda Mazda3 Problem
Average Mileage: 97,833 mi (81,500 mi - 108,000 mi)
Visitor, 2004 Mazda Mazda3, 108,000 mi
Engine seems to be "testing" more frequently than before. CEL intermittant and now permanent. Vehicle stalls after spending time at freeway speeds. Rough idle. Stalls or nearly stalls at stop lights. Hard start after refilling gas tank during long trips. No resolution yet.
Visitor, 2005 Mazda Mazda3, 81,500 mi
Once in a while the engine will idle VERY low and when the gas pedal is pressed then released to up the revs it may dip below where it was idling and stall.