Why would it do it on 80m in particular though? That has to mean something.
The SWR varies from one band to the next with a G5RV. High SWR means higher voltage and/or
current along the feedline for the same output power. The voltage/current distribution also varies
with frequency.
Say that the problem is a corroded contact somewhere: the more current through that point,
the worse the contact gets, and the SWR shifts. (And a worse contact may mean more power
dissipated, so more heating.) On the bands where that contact happens to be at a high
current point of a standing wave, the effect will be greatest. On another band the current may
be lower due to a lower SWR. Or the contact might be at a high voltage point on the standing
wave where the current is less. Either case will cause less heating of the contact.
Similarly the stress on the tuner will depend on the impedance it is trying to match and the
frequency (or, more precisely, the range of reactances available to use to match it.) Many
manual tuners tend to be less efficient when matching low impedances on 80m and especially
160m, because the limited maximum capacitance available forces a less efficient matching
solution, thus more heat generated in the tuner.