I don't think the system is very sensitive at all about tyre pressure. For reset I think it might be that you might need to drive the car, or drive further, after pushing the button to reset for it to get the message, switching the ignition off after reset might confuse it. If the light is on it's free and easy to try pushing reset this at the start of a journey plus you don't get your hands dirty or cold if the cabin is warm.
Or IF the system is run off the ABS sensors it might be an intermittent fault with one of those and IF the sensor or cog it gets its message from are exposed it might just be muck or rust on or between them, this means checking in the cold and probably dirty hands.
Another way to avoid the cold and dirty hands is to ensure the car battery is not at low charge so that any computer can start to play up, even if the car starts and lights seem to be bright enough.
I also favour the car battery reset as again it's quick, free and easy to do and if it doesn't work you've lost nothing (see vid below) - first check your Owner's Manual for anything that might need resetting or resynchronising, the tyre warning light will come on for a while after reconnecting the battery so don't worry about that.
The only other thing I've seen is that stupid fuse links on top of the battery can fatigue crack from car use vibrations so you could have a look at that for cracks, or crud at connections.
Good luck.