LED downlight remains on after switch is turned off
It could be the bulb circuitry going bad. LED lights are different in that most of the "bulb" is actually voltage conversion and a simple circuit system to regulate the LEDs. 

This is just an educated guess, but what it sounds like is there's a capacitor inside that still has power in it. The light bulb itself probably has something that senses when the power is turned off and turns the LEDs off via software, letting the capacitor just lose voltage through attrition. If that part of the bulb stopped working, that capacitor could still power the LEDs for a few seconds before running out of power.

You can test this theory in a regular lamp. Just turn it on for a minute, then turn it off. I don't know that it's dangerous to let it keep on doing this (it's probably been doing it like this all along, just with the cutoff working), it's just not expected behavior. If it doesn't overheat in the lamp I wouldn't worry about it.