There are reports of The keyless entry module on some Mazda's getting damage during installation of a remote starter . See disclaimer from DEI below : 

In these vehicles, the factory keyless entry module is sensitive to interference and may cease to operate without notice. Please ensure you disconnect the (-) terminal of the battery prior to disconnecting and reconnecting the connectors at the start-stop module below the steering wheel to avoid damage to the keyless entry module.

UPDATE :  I have been contacted by an installer that can confirm that the keyless entry module will start working again after a certain amount of time. Note* he did not unplug the car battery before any connections to the start stop unit. He also told me that a colleague he works with, did unplug the car battery and the keyless entry module still got damaged. Further info is needed to understand what is really  causing these issues.