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The sunspots do rotate with the rotation of the Sun, and the same sunspot can appear in subsequent rotations, but that's generally a rare condition rather than the rule. If it's a really large sunspot you can certainly see it again when it rotates around to face us again.
We've been in solar minimum, so the number of sunspots has been very small. We're approaching solar maximum in the next few years, so you'll start seeing more and more sunspots in many different locations.
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