If the garrison does not flee the building, either because they've held the attacker to a draw or beaten them, or have lost the combat but passed their Break test, then the attacker must withdraw from the assault, and is nudged directly backward 1". The close combat ends, and the attacker must launch a new assault next turn (which they may regardless of whose turn it is) if they wish another attempt at driving the garrison out. Note that a unit that attacks or defends a building in two or more consecutive turns does not count as fighting a new first round of combat.
The assaulting unit does not have to take a Break test if the combat was lost. The warriors in the attacking unit know full well that the garrison cannot run them down if the combat goes poorly and automatically retreat in good order with no chance of a rout.