Robo Rally cleverly avoids this trope, where indeed the robots become progressively more unreliable with each point of damage, until they finally explode.
This applies to the board game Talisman, as spells and attacks that outright kill enemies and followers only remove one or two "lives" from a player character's total. True player character death only comes when the last life is removed, save for a rare few "instant death" situations.
Magic Realm avoids this trope, where characters each have a number of chits that represent actions such as fighting, maneuvering and casting spells. A damaged character must disable a chit each time he is wounded, therefore damage causes a character to be less effective. A sufficiently damaged character may become helpless, as he no longer has the chits required to wield a heavy weapon or to duck enemy blows quickly enough. When all chits are disabled, the character dies.