How do you reckon the Dornish are able to keep two armies deployed, stationary, and fed for so long?

There’s a couple factors: first, the armies in question are smaller than a lot of other armies and they’re split up on top of that, so you only have to provision 12,000 in each place, which reduces the logistical difficulties immensely in comparison to the armies of the North or the Westerlands or the Reach. 

Second, Dorne is less agricultural than other regions of Westeros, with much less emphasis on the production of cereal crops. Their economy is more focused on the growing of lemons, pomegranates, olives (and olive oil), blood oranges, grapes (and wine), and peppers, the manufacturing of sandsilk and satin, the breeding of horses, and commerce. These industries don’t need the all-hands-on-deck of cereal grains, so Dorne can afford to have its fighting men away for longer. 

Third, stationary is easier to accomplish when Dorne isn’t actively engaged in the fight. With less economic pressure and no fight on its own soil, the only problem with keeping your men stationary is that they might get restless and bored. This gets more difficult when Oberyn dies and Dorne keens for vengeance, but Doran has been Prince of Dorne for decades and his grip on his subject is far stronger than the tv show thinks.