You cannot choose when to apply “Gyroid’s” effect. If “Gyroid” would be destroyed as a result of battle, its effect is applied (once per turn) whether you want it to be destroyed or not.
If “Gyroid” is destroyed, and is then Special Summoned again that same turn, the effect is reset and its effect will be applied again if appropriate. If “Gyroid” is attacked once, is not destroyed because of its effect, then gets flipped face-down, its effect is reset and will be applied again if attacked that turn.
The effect of “Gyroid” is a Continuous Effect that cannot be chained to (including “Divine Wrath”).
If “Gyroid” is attacked for the first time in a turn by “Dark Ruler Ha Des”, “Gyroid”’s effect is not negated because it will not be destroyed.
If “Gyroid” is equipped with “Heavy Mech Support Platform”, the effect of “Gyroid” will prevent both from being destroyed in battle. If attacked again the same turn and “Gyroid” would be destroyed, “Heavy Mech Support Platform” will be destroyed instead. A third attack will then destroy “Gyroid” normally.
If “Gyroid” is attacked during a Special Battle Phase created by the effect of “Last Turn”, and is then attacked again during the regular Battle Phase, it will be destroyed because its effect was already applied once that turn (during the Special Battle Phase).