i purchased the remotekey+ from eas and have the same problem.
when i don't lock the car the remotekey does not power off completely and when the car starts back up it shows battery /voltage low. I've been living with the issue for a year now and have double checked all connections / taps.
Alpine White E70 11 X5M - K&N Filter , STI Mag , LI , Self coded , Ultimate DP
Jerez Black E92 10 m3 - STI Mag| LI | RE SSK | AFE Filter | Fabspeed XFC / Xpipe | AA ECU 1.5v | BMW PSW | | Envy Charger | Megan Exhaust | Mich SuperSport | Self coded a bunch of stuff
Jetblack E92 08 m3 - V1 | RE SSK | RR Scoops | AFE Filter | AA ECU <Retired>