From a technical standpoint, it's a packaging issue. The space available in the engine bay and between the two front wheels means there is enough space for the manumatic in the 2wd Panda, while the output shaft location on the manual transmissions used in the 4x4 that connect to the rear driveshaft and differential means an automatic transmission would simply be too long to fit between the front wheels. The output shaft would be so far out that the front axles would have to be wildly asymmetrical in length, meaning torque would always spin one of the wheels more than the other. This is disregarding for a moment the fact that the output shaft would probably get in the way of the steering connecting rods; and also disregarding the fact that the clutches they currently have in their automated manuals and DCT boxes can't handle the stress of all four wheels having grip and would probably wear too fast, overheat, or simply break. While I'm sure a solution could be engineered, it would have to be a completely new gearbox and Fiat recently simply hasn't had enough demand that would justify investing in the research and development for that. That's the economic aspect for why there are almost no small 4x4s with autos. The same goes for the Duster in that not enough people would buy the 4x4 with an auto considering how much more expensive it would have to be.
As far as the 500x is concerned, the added space allows for them to use the ZF 9 speed gearbox, which really isn't that much bigger than the 6 speed manual (which fits into the TwinAir because the engine is smaller). That being said, the ZF box is a bit of a mixed bag because while it provides plenty of ratios to keep the engine in the optimal rpm range, it uses two dog clutches (basically a clutch with gear-like teeth that prevent slipping) so every time it shifts from, say, 3rd to 4th and 6th to 7th the shift has to be slower so that the rotating input and output have time to synchronise for the dog clutch to engage. This works well with dealing with the forces of trying to send power to all four wheels, but somewhat dulls the on-road driving experience.