Today I had an 32khz XTAL startup problem, that was obviously caused by a
too small load capacitance.  For the product it is essential that the
PIC always runs. Therefore I want to make further reliability tests with
the XTAL and caps.

What is the worst case condition for voltage and temperature, under which
a marginally connected XTAL is most likely to fail?

I have set the PIC to LP mode, if that matters.