If you pay attention to the battle at the end, Sandalak's archers were beginning to panic because of lack of infantry cover. But it's not a simple yes/no calculation, it's one that factors in various unit-specific stats.
Round 9:
With no infantry cover left, Evergreen Bows (3) panic and retreat.
With no infantry cover left, Proelium Dominus Guards (9) panic and retreat.
Round 10:
With no infantry cover left, Hail of the White Doe (5) panic and retreat.
Last round(12):
With no infantry cover left, Fern Leroux (4) panic and retreat.
