It’s hard to say for sure without seeing the location of the non-soldered joints and analyzing some of their characteristics but Amkor has done much work on POP and has published several papers on the subject.
Check out all of their white papers.
In particular, this white paper talks about the effect of die warpage and the use of a “dipping paste” to bridge the gap and overcome coplanarity issues. This dipping paste gives greater transcription vs. flux and can expand the tolerance band of the process.
Additionally, Amkor has done work on SOP (Solder on Pad) where the top pads on the lower package are bumped and also help to eliminate open joints.
I am truly NOT the expert on this but have spoken with Moody Dreiza once or twice and he is great. Suggest a call or mail to him for more help if needed.