I tend to relate mathematics to just about every aspect of human life. You just brought up a good one I've always shared with people.
I don't believe potential energy exists just in the realm of physics. We all have this internal love potential within us. We share this potential amongst the people we care for, and just like energy can only be transferred, we simply recoup the potential we make kinetic for the benefit of others through the receipt of it from others.
That said, someone who has fewer people to focus their potential on, such as myself, tend to put more effort into each of the few they have. For example, as someone with absolutely no ties to my blood relatives and few close people I would consider real friends, I very obviously put a lot of effort into those few people I do care about. It also makes it more difficult on those types of people when they receive, according to their perception, less effort (energy) in return from the people they expend it on.
From your description, I see a high potential for love that you shared slightly with multiple points of focus, which made none of them significant. When you found one point of expenditure to focus on, you focused it much more strongly than before, and you received in that final period of time far less (as you perceived it) in return than you expended. It also makes it harder to lose that point of focus because your expended energy seems wasted in your mind. No one likes to be overworked and underpaid.
I don't want it to sound spiritual or metaphysical, I think it's very logical. It's no different than a job. Your satisfaction with your job is proportional to the gratitude and compensation you receive from your employer. The less you are paid and the less appreciation you receive for your hard work, the less you are willing to work and the less satisfied you are with your job.
That's one reason I consider relationships of all types to be battles of effort, and the best relationships of all types are ones in which the parties involved expend cooperative, equal, and synergistic effort. Look at the AH conversations as a simple example. The best threads are the ones in which differing, even conflicting, ideas are expressed courteously and respectfully with regard for the views and backgrounds of others.