Definitely re-apply. It's been awhile, and chances are that you were simply not the preferred candidate at the time - perhaps there was somebody slightly better at the time, or simply too many to choose from. I had 300 applicants for a junior admin role recently, and filled the role within 4 days of advertising. Many applications arrived after that time, but quite frankly I didn't have time to sit down and go through them all - I'd already found a great candidate. I may need to advertise another admin role within the next few months, and I hope good candidates will re-apply.
On the other side of things, unfortunately I have undesirable candidates who re-apply constantly, even applying multiple times to the exact same advertisement (yes, they're not even keeping track of what they're applying to!) They'll never be successful, but it's not appropriate for me to contact them to explain that they're wasting their time.