If my army constitutes 15% of the total army, but 40% on the battlefield
and reinforcements trigger below 40%
it follows that my army will be spent long before the battle is over.
Holding back my troops and let my ally fight alone will lose us the battle, because on his own he is outnumbered, also I have to engage the enemy just to lose men and trigger reinforcements.
edit: I've fought this particular battle several times to see if I can get better results, but it always ended like that. The trigger mechanism was even more problematic because the enemy AI was mostly defensive and had to be attacked at his spawn point. Pulling back my army to our own spawning point to trigger reinforcements there was quite demanding. I liked it, it was very tactical. But the losses!