PLEASE CORRECT ME IF I'M WRONG - but, aren't there two things going-on in the credit card sized remote...? The active aspect of remotely locking/unlocking the vehicle from a distance (requiring batteries) and the passive aspect where it's the VEHICLE that emits the signal that detects the presence of the chip in the remote for the proximity detection to allow the door requester buttons to lock/unlock the doors and for the keyless ignition to work. I am fairly sure they act similar to company ID badges that you waive near a scan pad - the scan pad provides the signal and searches for the responding passive identifier.
Having said that ---
I have found that (for some reason) having my company door-pass near may wallet (where I keep my Mazda key-card) will not allow me to enter my vehicle or start it - I need to keep the in separate pockets or they will interfere with each other... even though they are both passive.
Have you changed anything with your wallet...? anything new that might interfere...?