I haven't looked at the code of vBulletin for about a year now, but this would be the theory behind it.

select count(*) from table where date="donnodateformat" and username="$username";

mysql_query(...)

if(mysql_num_rows($result) = 3){
print "sorry dude, you've had your 3 posts.";
} else {
leave the posting code in there that is already there...
}

You'll have to go through and look up the details like the table name and there columns etc - but that would be a basic approach to work on.