I was looking at an old post of mine and noticed that it received a down-vote. Is there a way to see why it was down-voted, perhaps to allow for further clarification on my part?
As noted by various commenters, there is no way to see why one was (or who) downvoted. See this meta post for more details. Generally speaking, downvoters are encouraged to leave comments explaining themselves, but no one can make them do that.
Often times, the downvoted party will leave a comment asking for clarification, but in situations like this (an old post that hasn't recently been bumped), it is not likely to generate a response from the anonymous downvoter.
It's also worth noting that there may be comments already on your post which the downvoter may have upvoted ("this comment adds something useful"), which would be a reason why a new comment was not left. Either which way, if you would like to clarify a post, you should be using the other comments as feedback even if no one has downvoted the post.
Additionally, and I'm not sure that this is done often, consider asking other people in comments to the post (or maybe even Chat in some cases) what they think about the answer, as to why someone might have downvoted, and I'm sure those people can also help direct you in the right direction.
In this particular case, the only post of yours that fits what you have described is this one. In that case, there is a comment somewhat critiquing your answer and there are 2 upvotes on that comment. You responded to the comment, however, you wrote that you had forgotten the source for your defense. If I had downvoted (I didn't), I might have just upvoted the critiquing comment without leaving one of my own.