Yeah, I don't think this standard behaviour.
I place the transmitter in dock, it flashes red briefly then turns solid green (or flash green if charging). All appears normal.
At some point, it can be 5 minutes, sometimes a few hours, it'll start flashing red again, but it flashes in a distinctive pattern, not just on-off-on-off. It flashes 4 times (approx 0.5 second each flash), then the LED is unlit for approx 4 seconds. It'll continue flashing red like this until it's undocked and redocked, after which it'll reappear again.