The activated ability that Gigantoplasm gives itself doesn't have a duration. It lasts until Gigantoplasm leaves the battlefield or another effect overwrites it (for example, if you activate the ability again once you have more mana available). Each time the ability resolves, it will overwrite any previous effects that set its power and toughness, including previous activations of the ability. Effects that otherwise modify Gigantoplasm's power and/or toughness, including +1/+1 counters, will still apply no matter when they took effect.