Hi! This is a great question. I'm sure I haven't had as much work experience as some of the other professionals who could comment here, but I wanted to at least give you the start of an answer to your question, so I'll share a few thoughts and then I have a few links for you.
In my opinion, it really matters why you're feeling burnt out or uninvested. Is the workload too high? Is the company not a good fit for what you want? Is the career path not a good fit for you? Or is it related to personal stressors in your life (for example, if a relative is sick, you might not feel invested in your job as much because you're worried about his/her care). The answer to this question likely determines a solution. If the workload is too high, you might talk to your manager about reducing it or find better ways to prioritize. If the company is not a good fit, you might apply to other jobs in your field. If the career path is not a good fit, you might try to start a fresh path, either by going back to school or applying transferable skills to a job in a related field. If it's not related to work, you might let your manager know a little about what's going on (no details, just enough so he or she is aware that your life is getting extra stressful for the next few months or however long, or reduce your hours).
I'm going to refer you to a few links from askamanager.org, which I think is an amazing workplace blog. I'm doing this to give you more details on a few of these possibilities, and to show that this is a good question that other people have and will struggle with/ask about.
http://www.askamanager.org/2014/02/i-think-im-in-the-wrong-career-does-my-interviewer-expect-his-new-hire-to-fail-and-more.html (the first question) http://www.askamanager.org/2012/08/im-burned-out-at-work.html