I'm going to agree with both Oz and Arria here. I can't tell you all the number of fights I've started based off the fact that I will honestly admit to loving and still having feelings for a past partner to my current lover. I consider the word "love" to be a feeling whose scope cannot be diminished by the short amount of time in a life, and whose infinite nature cannot be exhausted by volume.
However, a feeling and the commitment to sharing it are two different things, and it's the commitment part that is finite and therefore tricky to keep a handle on. It's also the actions as opposed to the intentions that I see causing a split in this thread, and where the poly and the singularly devoted folks start to break ranks. Love is infinite, time just ain't.
Oz is right: having one child after another doesn't mean you love the second or third one any less and it doesn't mean that love is taken from the first either. However, time gets divided, so do resources. Eventually there will come a point where the kids cannot be taken care of or loved because there just isn't time or money or whatever in the day to do so. At that point you can feel all the damn love you want for the kids, but are they feeling it from you??
When I fall in love, personally I become pretty damn fixated on the moment to moment happiness and pleasure of the person I'm with. I pay a LOT of attention, I give a lot of myself. I simply don't have the time or frankly the strength to give that to anyone else save in small doses of affection here and there. I can feel a lot of love, sure, but I also feel like I can only express it in a way that seems worthy of the emotion of being "in love" to one partner at a time. This doesn't mean I follow J around 24/7 waiting for the opportunity to be of service to him, it simply means when he wants me I need to feel, for myself as much as him, that I can drop anything and everything and be by his side.