Good point. Using answer mode because did not fit in comments.
But when you wrote about trace gases I thought that there are indeed traces gases in the Jovian atmosphere and a descending probe has some probability of hitting a cloud deck made of
NH4, then NH4SH, NH42S, and finally water clouds. Are these sulfur compounds nasty for the majority of membranes?
But I worry too about temperature, surely the hydrogen supply would need to be preheated, and oxygen exiting the tank would lose temperature too due to pressure drop. Or are there any fuel cells that operate well at low temperatures?
FYI the possible design would be a quadcopter assisted by an infrared balloon
(derived from https://www2.jpl.nasa.gov/adv_tech/balloons/outer_jupisat.htm)
The quadcopter would need at least 6kw of power for a 10kg descent module to just hover in free fall conditions due to high g (in the case there is a balloon failure/malfunction). That's quite a lot of power. So the cell stack would need to be lightweight and compact (less or equal to 1kg and 1l volume would be ideal)
A 2L oxygen tank would provide the fuel cell up to 12kwh of energy at 80% efficiency. that would be enough for 2 hours of hovering, so the best would be to have it assisted by a solar infrared heated balloon. (a big one, pumped with hydrogen taken from the atmosphere, and may be preheated before pumping)
The thermodynamic equilibrium temperature could be modeled taking into account, heat gain from the fuel cell, heat gain from joule losses and payload, heat loss from gas input temperature and heat loss from the enclosure. As the probe descends, the problem would be reversed, heat gain would come from Jupiter atmosphere, and H2 inlet temperature and pressure would be significantly higher and I think the efficiency of the cell would be better. At some point however the valve would need to be closed to prevent pressure and temperature damage. Maybe an empty lightweight tank could be filled just before to make some reserves for the late descent.
At this point, the probe is on final reserves and then secondary battery power (presumably not much capacity, only for science payload and critical systems at this point) and is sinking.
With that design, the probe could stay operational in the atmosphere for 72 to 96 hours, maybe.