What would you do in my place? I'm an intern, the money is good and the total conditions are awesome. But it's not what I wanted at all. I really could use the money now but I'm afraid that this will not contribute to my experience as a developer in the long run and might even hurt my chances.
It never hurts to have an understanding of infrastructure as a developer. In fact, it's often a bonus when you can convincingly argue a point with a sysadmin if you ever end up in a big corporate environment. Also understanding the infrastructure environment that you will be developing for can only aid you as a future developer.
However, I would press on with the polite reminders to your management about being a development intern and make sure you communicate to them that you expect them to transfer you to a development position as soon as is practical and that you consider your current situation temporary.
You are at the beginning of your career - soak up the knowledge and experience of where you are, but keep your goals in mind.
This is remarkably unprofessional of the firm. Along with politely reminding them that you consider the situation temporary and should expect to be moved into development in a reasonable time frame, you should quietly start looking for a new internship. Don't consider a permanent position with this firm, they have problems keeping promises.
While having IT infrastructure understanding/knowledge as a developer is absolutely a great thing and can improve your marketability; having only this experience on your resume can make it more difficult to attract attention for the types of positions you want in the future. You will need to take more care in drafting cover letters and in interviews to explain how this experience makes you more valuable as a developer.
I speak from experience though in a somewhat different scenario. I'm a self taught software developer since childhood, with some professional experience (freelance work and one published video game). I went back to school after having kids and graduated top of my class with a degree focused on embedded system design (hybrid electrical engineering and software development).
When applying for internships in embedded systems with companies that had a hand in the creation of the program: "Based on your experience, we'd like to offer you this other [purely software development] internship working on our website..." The internships I was interested in went to straight EE classmates with no prior experiences.