I know, that sounds really selfish. But as I dive in, you'll see it's not quite as bad as you think. Let's be honest, first off. Most things that you do in life are to benefit yourself in some way. If you think about it, it's true. Why find a lover/partner? To not be lonely. Why do the dishes for that partner? To make them happy so when you ask something of them, they'll return the favor. Etc, etc, etc.
Anyway, on with the post. Step 1...
Sharing is caring
It may take some time, but through a few casual emails, you can get your reviewer to open up to you by sharing tiny bits of yourself. They'll see that you really are a human on the other side of the text, and start to connect with you.
You have to want this. You have to. If you do not truly want to connect with this human on a personal level, you will stop giving a shit, and you will let the relationship fall by the wayside, and they will recognize that emails coming from you only mean you have a new piece out that you want to thrust at them.
Remember the important details of your reviewers, or the details they feel are important. Where they live, brothers & sisters, a new job they're applying for, what degree they're attempting to obtain in school, a book they're working on, new house, etc. Follow up on these items with them through email to show that you were paying attention, and you do care if they got the job, got the house, finished school, saw their family for the first time in years.
Remembering details of many people can be difficult, so fortunately you have email history to look at, and you're never, or rarely ever, put on the spot to remember it without being able to reference said emails. I do this sort of thing for a living at my job, so it's become second nature to remember a ton of details about what's going on with 20-30 different people at a time... which reminds me, I need to follow up on something when I get in the office tomorrow morning ^_^
I know it's a strange thing to say, and it's a hard mentality to develop, but learn to actually care. My boss taught me this. It's not enough that you asked, and remembered, and follow up later, then acted excited for their success, or downtrodden for their failure... You must actually give fucks about them and their life.
You'll notice if they're interested in you, and connecting, they will do the same. If, after many attempts, you notice they're not interested, gauge your desire to have them on your side. Ah, I say on your side... but truly that's what it is. When it comes down to it, and you have a new work that you'd like to share with them, and they have a very busy schedule, they'll be on your side and find the time to make it happen.
Anyway, gauge the importance of this potential relationship. Do they enjoy your work, or was it just so-so to them? Is their review/writing style on par with how you like to communicate to your audience? Do they have a wide reach, or a large audience? After answering yes to all three of those, I would say continue to pursue them, gently... don't be overbearing and email twice a week, or overshare. Perhaps, even come right out and ask them, "Are you interested in maintaining a relationship with me outside of the author/reviewer relationship we have? Because I am." Maybe they'll go, "Hey, shit, I didn't realize that's what you were trying to do... totally, I'd love to!" or... maybe it'll be like, "Yeah I don't have time to email you about personal stuff." and if that's the case, just be like, "Totes cool. In the future, if I have stuff for reading, would you like me to contact you?" And then all that awkward courtship stuff is over and you can move on to fostering the relationships that really matter.
Welp... I better get my chunky butt off the couch and go for a run or something >_> have a good Sunday kiddies!