Síndrome de la vaca caída.

Sometimes they are on their side, sometimes they are squatting. In the latter case it's called "Vaca caída en estado de alerta":

"3.- VACA CAÍDA EN ESTADO DE ALERTA (O SÍNDROME PARAPLÉJICO PUERPERAL, O COLAPSO ATÍPICO) [...]
Esta forma corresponde a la descrita por los autores anglosajones como Alert Downer o Downer Cow Syndrome (Síndrome de la Vaca Caída)."
http://www.produccion-animal.com.ar/suplementacion_mineral/3...
This is a document about "vaca caída".

"There are many reasons that cows go down"
ASK any other dairy farmer or a veterinarian, and they will tell you
that a down cow can be either the most enjoyable case they have
treated or their worst. With some down cows, a simple bottle of IV
calcium will get them up and back on their feet, while, for other downers, no matter what you do, nothing seems to help."
http://www.downcow.com/pubs/dairyjournals/reasons that cows ...


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Note added at 30 mins (2012-04-02 17:40:35 GMT)
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"Síndrome de vaca caída ¿cómo proceder y que esperar?"
http://www.engormix.com/MA-ganaderia-leche/sanidad/foros/sin...

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Note added at 1 hr (2012-04-02 18:26:08 GMT)
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síndrome de la vaca caída:
https://www.google.es/search?q="síndrome de la vaca caída"&n...

vaca caída:
https://www.google.es/search?num=100&hl=es&biw=991&bih=601&q...

vaca postrada:
https://www.google.es/search?num=100&hl=es&biw=991&bih=601&q...


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Note added at 1 hr (2012-04-02 18:29:23 GMT)
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These results show that the common term in Spanish is definitely "vaca caída". "Vaca postrada" is rarely used.