Others have responded to the core of your question, i.e. (how) can you find out who is serially downvoting you. I thought a slightly broader perspective might also be useful.
It's worth noting that SE uses algorithms to detect suspicious voting activity, which doesn't just include serial downvoting, but also serial upvoting. The underlying principle is that posts should receive votes based on their usefulness (or lack thereof) rather than on the identity of the poster. Serial voting of any kind is not only unfair, it undermines the integrity of the site.
Some serial voting can be somewhat innocent, committed in ignorance of the algorithm and lacking insight into how their activity is unfair. For instance, an inexperienced user might like another user's post, and upvotes it; they click on the username to read their profile, and they discover that the profile page lists other posts by that user. They click on some of these posts, like what they read, and upvote these posts too. It's an innocent act, and if it's only a couple of posts voted on then it's harmless enough. But if they upvote (say) a dozen posts by that user, this is giving that user an unfair boost in votes; thankfully, the algorithm is likely to identify this as serial voting and will automatically reverse the votes.
Of course it can also happen somewhat innocently with downvotes. For example, I might notice that a particular user has been posting ignorant, misinformed and incorrect answers. "Who IS this obnoxious person?" I ask; I look up their profile, and look through their recent posts, which only confirms my view about them, as I DV more of their answers. The point is that even if I'm assessing each of their posts on its merits, the fact that I'm selecting just their posts for review means I'm serially voting, and if the combination of the pattern of my voting and the number of votes cast meets the algorithm's parameters, it will automatically reverse those votes.
It's also worth noting that the system does NOT alert the mods when it identifies suspicious voting behaviour and reverses a user's votes. I know this because two years ago I became concerned about a particular user whose poor (and in some cases, glaringly ignorant) answers were consistently receiving many times the number of votes that my own awesome answers were getting, and when I looked at their posting timeline in their profile I could see not only that there was an obvious pattern to the significant upvotes they were receiving (which regularly exceeded 100 rep points a day), but there had been several very large voting reversals in the last six months. I could also see that there were several occasions where serial voting was clearly occurring but wasn't enough to have triggered a system response.
I don't know whether the user had created fake accounts, or was using the keys to the legit accounts of other household members, but the upvoting was too concentrated to have been from a more innocent cause such as in response to them tweeting their answer. They were clearly cheating. But looking at the size of some of the reversals - 500 rep points or more! - I was amazed that the user hadn't been suspended. I learnt that I had to flag one of the user's posts and alert the mods to my concerns. I'm pleased to say that when the activity continued, the user ended up being suspended for a year.
The point is that (a) mods aren't alerted when the system picks up serial voting and reverses the votes, (b) the system doesn't pick up "less egregious" serial voting, (c) mods can and will take action if you alert them to obvious serial voting (although if you can't identify the user, their only recourse is to refer it "upstairs" to staff), and (d) if a user knows about the system algorithm and genuinely wants to target you, it's not too hard for them to structure their serial downvoting (or, indeed, upvoting) so that it flies below the system's radar and cannot be detected.
Apart from flagging your concerns to the mods, the best defence against serial voting is for all of us to vote vote vote. If all useful posts are receiving plenty of upvotes, then on any individual post a single DV from an antagonist will be lost in the wash.