Just as all eligible units (i.e. those in base contact with the enemy) must fight in close combat, similarly all models in base contact with an enemy must fight. Models cannot elect not to strike, nor can they normally be prevented from doing so.
Occasionally a spell or special effect will stop models from fighting, but more often will simply reduce a model's chances of landing a blow – the will to survive is particularly strong when a six-foot-tall, heavily muscled killing machine is laying about you with an axe.