How automated is it? Any parts that could be automated that aren't? That would be step 1 I think.
Secondly, don't panic!
Thirdly, consider if I sell you my Starbucks card balance and I was evil, could I some how phone Starbucks up and say my card was lost/stolen? What happens in this instance? It's the biggest risk you need to look at from what I can see at first glance. Perhaps test this.
Fourthly, is there a difference between a gift card and reward card? Coincidentally we just bought a reward card today for our startup (we drink lots of coffee). It looks like it has a similar number format as a gift card, and the Starbucks FAQ says they can refund a balance from the moment it's reported as stolen/lost:
http://www.starbucks.co.uk/customer-service/faqs/card
Fifthly, become aquainted with the law. Gift cards in the UK at least are considered as "Like cash" as far as I am aware. This means you could be setting yourself up for a bit of legal trouble down the line if you are considered a transmitter or money or such. As other posters point out, the reason for your early success could be because you are being used as a money laundering service without you being aware of the fact.
And a question, what exactly are you doing with all these cards? Selling them on somehow? Or keeping them?
If this is too much risk/pressure for you, and you feel out your comfort zone, consider selling it as is for BTC. I'm sure you'll find a buyer for a good sum. If you like risk, want to make some money then good luck! Let the adventure begin. Although it sounds like as soon as you get any volume and Starbucks catches wind you'd be pretty easy to shut down. That's one of the better outcomes for you as well I think, the legal risks sound significant. If it was mine, I'd look for a quick sale and pass the risk on.