I recently had the same problem with a Safe-T-Alert detector. Mine was showing a malfunction alarm when the supply voltage dropped to ~11.5 volts. I called the manufacturer (MTI Industries) and was told that they had reports of this problem. The detector was only a few months old and still under warranty. MTI sent out a replacement unit and when I received it, I sent the defective one back to them. I tested the replacement on a power supply down to 9 VDC, and it didn't show a malfunction alarm.
I should probably also mention, that when I had the malfunction alarm on the detector, the battery voltage was at ~11.9. I was load testing the battery, and had almost everything that ran on 12 volts turned on in the trailer.