Variation in parental care is interesting, I don't think the Flamingo abandon its eggs everytime, I read the parents usually share the incubation but desertion may occur (see http://www.jstor.org/discover/10.2307/1369487?uid=31975&uid=3738328&uid=363756311&uid=2&uid=3&uid=31974&uid=67&uid=62&uid=5911992&sid=21106399071351). (PS: Prof. Cézilly was one of my previous supervisor, and he is specialized in bird behavior, and he worked a lot on flamingo, you may ask him from me).
If you want to read more about brood desertion I would recommend this article
Does it really abandon them or only goes away for a while?
In Vanellus spinosus we can see the both parents going away for attract potentential predators to themself and s a consequence to protect their chicks and eggs. May be the facts you remarked with the flamingo is the use of the same strategy.
We have witnessed egg (colony) abandonment here in United Arab Emirates. Birds leave en-mass from the colony and we have not seen them coming back. In our conditions it is usually disturbance from predators and very high temperatures in summer months (reaching almost 50C) when the birds have left. At sites with problem of predators like dogs and foxes, colony abandonment by incubating birds is common.