I am a new user and I have already answered 19 questions. What annoys me is that in most cases the person who has asked the question does not revert back to accept an answer. I am pretty sure that if not all, most of my answers were pretty helpful. This is most relevant especially in cases where only I answered the question. Shouldn't this be monitored?
It is monitored, sort of. The community tends to self-police (at least on other SE sites, I haven't seen it too often here but I could just be missing it). In other words, person A asks a question and somebody comes along and leaves a comment "Hey, I would like to answer your question but you have a history of leaving answers unaccepted. If you accept answers on other questions, somebody might be more interested in answering this one."
In other words, if somebody consistently doesn't accept an answer, then stop answering their questions (and if you post a friendly suggestion as a comment, others may stop answering also). And the person may correct their behavior and accept good answers.
You can also post a comment like Kyle suggested. Just be polite while posting the reminder. Assume the user is just a beginner who is unaware of how the site works rather than the user is lazy or abusive and maliciously leaves things unaccepted.
It's sometimes easy to identify questioners unlikely to accept an answer. Do they have many unaccepted questions? Are their questions homework? Do they answer other peoples' questions? There's probably a lot more clues than that to figure it out.
So -- if you find yourself consistently getting burned by answering questions that never have any answers accepted, consider changing which questions you answer. Of course, that's if it bothers you at all. Maybe you're just happy to contribute to increasing knowledge for others who visit the question. Then it shouldn't matter whether it is accepted or not. All that matters is the usefulness of the answer.