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Becoming a ruler. If you step down after not ruling long enough (about 3 months, I think), you lose royalty. If you leave the realm or island, you lose royalty.
I'm not sure it's 90 days. Might be 90 days if you step down. I think a month is enough if you are defeated by elections. I vaguely recall it having a bunch of arcane nuances, but in some situations not being all that hard to get at all.