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TPS65131: Regulator not always turning on

Part Number: TPS65131
Other Parts Discussed in Thread: TPS7A39

Tool/software:

Hello,

I have a design that uses 2 stages of power regulation with TI chips. I have noticed that maybe 5% of the PSUs from my production run don't reliably turn on.
In this "failure mode" only the positive rail of the TPS65131 will come online.

Luckily it will usually work if I cycle the power a couple of times, and then it will reliably turn on if I cycle power in the next 10 mins (I'm guessing because of a small amount of residual voltage in the caps).
However I need it to just turn on reliably each time. 

Can you see anything in my design that might be causing this?

Here is the voltages I see in failure mode:

TP1: 5.2V (correct)
TP2: 14.7V (correct)
TP3: 0.03V (should be -14.9V)
TP4: 0.04V (should be +14.3V)
TP5: 0.04V (should be -14.3V)

Total load on each rail is approximately 85mA

Also in this design: TPS7A39