For low temperature, the amplifier in the feedback loop misfunctions. Monitor the voltage to the VCO control input. Also try characterizing the VCO by itself at the low temperature. Measure the frequency for different control voltages at room temperature and at -40.
The vibration problem is mechanical. Something in the circuit open or shorts. Or the VCO frequency is varied by shock.
It is possible that there is a big variation in the VCO frequency. Try to change the pll output frequency (change the comparison frequency for example) and see if the pll lock at lower frequency.
You must do what flatulent suggests. If at -40 degrees whatever, the tune line for the VCO is at 14 volts, and the power supply rail is at 15 volts, then the loop unlocks because what the VCO really wanted was to see 14.5 volts but the op amp can not get there.
I agree with biff44.
Usually a VCO is done with a LC oscillator. When you change the temperature the L and C value change. If you have an integrated VCO (integrated L and C) there are big variation (order of +/- 20 % of each value) in the values than change the oscillation frequency. You need to see the voltage in the filter loop: for sure it is near Vcc or ground. You can try to change the reference frequency in order to lock the PLL, but if the VCO has changed too much its oscillation frequency you will not synthesize your wanted output frequency.
So, what happened? Did you find the reason the PLL unlocked at -40????
Most likely reasons you have vibration induced sidebands:
1) your reference crystal oscillator is onboard and has vibration induced phase noise
2) your free running VCO has a lot of vibration induced phase noise AND
a) you have insufficient open loop gain, or
b) you have insufficient loop bandwidth