It was hard, but after some work all the components look good and no shortcircuits were found with a multimeter.
Anyway, It looks like it is not going to be easy and I get normal blinking and voltage values for up to 5 seconds, after that tension from NCP1117 drops to 1.5v and LEDS start fading out. NCP zone goes pretty hot so my first though is that any component is putting 3.3v line to gnd after boot up.
Yeah, it sounds like you have a short to ground somewhere. check the RN52; they're easy to bridge. And it sounds like that might be the culprit, if you have code uploaded to the 328; it takes a few seconds to turn the RN52 on, and at that point is when you seem to have trouble.
If you want you can post pictures of your module; maybe there's something we can see?