I think morale goes down, and the ones that desert first are the ones with the lowest morale, but it's otherwise pretty random and you aren't told which ones do.
Kill off weak units in "senseless" or "harrasssing" battles to avoid some nasty surprises. (Like loosing 8 elephants -as arcos- one round before you attack a big opposing army.)
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One rescue a day... that's my motto. - Deathstalker II