First of all lets start with block diagram of the analyzer.

Input signal goes through input attenuator. Than 1st, 2nd 3rd and 4th mixing. So frequency instability is most likely due to local oscillators frequency drift.

More detailed block diagram shows that 3rd and 4th local oscillators are in fact crystal oscillators. So their stability should not be an issue.

That leaves 1st and 2nd oscillator to look at. 2nd one is Dielectric Resonator Oscillator (DRO).

While its stability might be an issue, since its temperature drift might be severe, it would not correspond to observed instabilities.

That leaves 1 local oscillator as the main suspect. What is more the r4131d version that offers better frequency accuracy differs with additional AFC circuitry attached to 1st local oscillator.

That sums up problem identification.