I'm a little surprised how harsh some replies have been -- but not all. I agree with the folks who say to find out, before you punish him, whether he is actually being bullied, or has an issue with some particular class (maybe he feels horribly pressured in gym if he's not particularly athletic, or panics when it's math test day, etc.). If you keep tabs on his school life, how he feels about classes and classmates, which subjects' homework seem tougher or easier for him, you'll have an idea of whether he has some issues that would make him want to miss school. And as someone else said, look for a pattern -- were the sick days actually days that something was due, or he had a test, or it was "run the mile" day in gym, or the whole school had a standardized test (those are creating a LOT of pressure on teachers in some places, and the teachers pressure kids -- it's happening here)? Etc., etc.
He may indeed really believe he's "sick" if his nerves or worries make his stomach clench at the idea of going to school. I'd ignore the claim of vomiting since it was one time and there's no way to prove he did or didn't vomit.
Talk to his teacher in detail, describe what's going on here, and try to go over the days he was out and what the teacher says was happening that day or the day before. Ask the teacher what she or he thinks -- does the teacher have a good "read" on your child's personality? Could it be conflict with the teacher herself? Or is the teacher aware he doesn't get along with certain kids and is possibly being pushed around and just reaches his limit about once a month? Does he tend to give up easily on other things? Does he tend to procrastinate on schoolwork, which could mean he's got things due that he isn't telliing you about?
He could indeed just be blowing off school for fun, as some posters are indicating, but before you start disciplining him, rule out real causes and fears.