Yes, it works normally. Things have evolved in the technology of security systems and now it is standard to have any LED turned off on any motion detector (the LED's are now used for walk-testing only), the standard DSC and Honeywell wireless motions also do the same thing.
- This is a normal function for your motion detector. It's also a great power saving function since most of the current draw on the batteries is when it's transmitting a detection signal so if you're home and moving around it will only transmit every few minutes instead of every second, saving on battery life significantly (up to 5 years on average) but after the 3-minute lockout the passive infrared scans continuously until it transmits another motion signal.
Reason: most burglaries are done by someone who has been there before, if they see the LED then they know the motion will catch them moving in that given spot, then they can "map-out" where it's safe to walk (where the LED doesn't light up) for when they plan to return for a robbery.
You can also make this device "more sensitive" by moving the jumper pin position by the right side battery and having the back mounting plate mounted using the bottom screw presets so it faces slightly downward instead of straight forward.
Helpful tip: Change the batteries every 4 years if you're using Alkaline (dead or not) since the detector was engineered "too energy efficient" and the batteries actually leak and corrode the interior PCB at about the 5-year point on about 15% of the detectors with factory original duracell batteries (from what I've experienced in field service).