Well, since the thing switches off after a few cycles and stays off for almost a second I guess it's not strange that the voltage across C6 drops. I didn't do the math but there are 2 1M resistors from the mains so it could be totally possible that the starting voltage is a lot lower, somewhere around 5V maybe? My Chinese is non-existing unfortunately.
Edit: It looks like the voltage across C6 slowly rises and then suddenly drops, almost as if D6 is reversed

The slow rise could be the 2M charging C6 but why the sudden drop?
D6, R3(?) and the winding must be ok otherwise the mains would not be rectified.
Edit 2: After playing with Google translate I found the following:
Startup current is only in the uA range, working current around 2 mA. Further, if VDD drops below 8.2V it will go into undervoltage protection mode and switch off.
So... Why can't it power itself? D6 and C6 measure ok but maybe it's time for a blind replacement...