Paying cumulative upkeep is always optional. If it's not paid, the permanent with cumulative upkeep is sacrificed. Partial payments of the total cumulative upkeep cost can't be made. For example, if Mystic Remora has three age counters on it when its cumulative upkeep ability triggers, it gets another age counter and then its controller chooses to either pay {4} or sacrifice it.

Cumulative upkeep is a triggered ability that imposes an increasing cost on a permanent. "Cumulative upkeep [cost]" means "At the beginning of your upkeep, if this permanent is on the battlefield, put an age counter on this permanent. Then you may pay [cost] for each age counter on it. If you don't, sacrifice it."