No, you should not break off the relationship! YOu two have two children.
Okay, so, what can you do? First, you can cut him some slack. It could be a hormonal shift as a result of age. Teenage boys can orgasm at the drop of a hat. As men age, it takes more. The same sort of timeline exists for sexuality in a relationship. AS the relationship goes on, you become used to your partner. The newness wears off. 2 years is about right. Now, let's add on another factor: a brand new baby and a one-year old. How much sleep is your BF getting? How much pressure does he feel to provide for his family?
Sex is very complicated for most women. We tend to need more lead up time, hours really. The right movie, the deep conversation, candle light, etc. Men don't need all that, so we women tend to forget that sex is complicated for them too.
Okay, so what happens if he doesn't even what you to touch him? Then you start reading up this entire web site, especially the sections about what happens when baby makes three. Babies disrupt marriages in ways parents never dream of. Men feel left out. One or both spouses are too tired for sex. Men get worried about money and may spend more time at work. Women feel scared witless and want their husband's support. Understanding the dynamics is one step towards saving the relationship.
The good news is you obviously aren't so absorbed in the babies that you have no time for him. Even if he didn't reach orgasm doesn't mean he didn't enjoy and appreciate it. FWIW, my BF sometimes doesn't but he assures me it's not me. Just as I often don't, but I still really love sex.