>> The PIC should run when Vcc came back up > BOR
> 
> Unless you are right on the threshold and noise is continuously
> triggering the BOR!  i.e. PIC starts up, initialisation code starts
> running, small glitch caused by changing port state resets PIC.

That would be easily determined with a scope. Don't know how
others would do it, but I'd try a signal generator with adjustable
DC offset as Vcc to find the nature and limits of BOR. That's
assuming the PIC does in fact recover from a BOR reset
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