When I finally got Summoning of Fire Elementals to work, I was losing gold quick because I'd recently conquered some cities. Soon I was in the red and seeing messages about desertion. My Fire Elementals (which are really trolls if you haven't tried it yet) were soon unable to be clicked, like trained units who have deserted. (their unit tends to remain as a sort of ghost on the map)
I think being in debt causes even Summoned units to desert and I don't think this makes sense, to be honest. They should not leave my military service to join the population of a city. While I can think of ways that Fire Elementals could become gainfully employed, say as blacksmiths and bakers, they would be a fire hazard at the same time and I don't think they'd be accepted by the community 
I wonder if Ebbenwolves adopted by quests have also been known to desert? Or charmed spiders?