There are certain situations that make me sick of being around people, so the regularity (or lack thereof) of that feeling depends on how often the situations arise. I have a tendency to only make friends with introverts and introverted extroverts (and I'm kind of a low-energy extrovert), so very few of my friends force me into positions where I can't just leave a social situation when I feel like it. However, pretty much any time I go on an extended trip with someone (especially if that someone is an extrovert!), I get sick of them after the first day or two. It's never personal, but I find myself craving some -- any -- time to myself. On my most recent road trip (with an ENFJ), I actually got into a big argument with him near the end, and it wasn't his fault at all -- it was me being really frustrated and cranky.
Exceptions: when I travel with family, or when the traveling allows for some alone time on my part -- or for visiting other friends in the middle. Sometimes (and I'll bet this is an extrovert thing), going from one social event to another can be as refreshing as going from a social event to alone time. It's like how after a long day of walking, changing into a different pair of shoes can feel wonderful.
As for getting tired of dealing with people's wants -- that happens much, much more often.
I think it's due to lack of Fe. I am very quickly drained by dealing with other people's problems -- and usually I avoid those situations entirely unless 1) I know the payoff (in terms of a good relationship with the person, etc) is worth it, or 2) I am good friends with the person (meaning it's my duty to provide for them if they need it).