Me: "Because life is good even if it's painful"
What about when it's not good? We strive to make changes and fulfill what's empty. Then you question, why even do that? What happens when things go wrong again, or when it's not enough? What do you live for? Is it the next pleasant moment/period of life?
I don't think I can apply my situation to all situations, it could be more unique. But my recent experience was this:
Before I resolved my "life problem," I was so miserable and depressed that no matter how GOOD things were (i.e., no matter that I had a comfortable existence, money, a family that loved me, friends, opportunities, etc.), I was suicidally depressed and spent each day asking myself why I even bothered to be alive. Literally. And I think in that context, the existential questions tower to a mountainous size.
After I resolved my life problem and moved forward, I found that I experienced a "base level joy" so all-encompassing that I no longer even needed to know the answers to those existential questions. I'm happy to be alive anyway. The desire to live exists without any need for intellectual support. And I can still acknowledge that I have no deeper insight into the "meaning of life"... but that question no longer seems to matter that much. Yes, I will die one day. No, I am not exactly what happens to me when I die. And no, I'm not sure I will ever achieve anything "great." But life seems to be about knowing who I am, being able to be who I am, and interacting with others in a way that they also know who I am and I know them; and enjoying what I can along the way.
I think a lot of people are content with who they are or secure enough in themselves and their lives that they don't need to answer those impossible questions, at least not as a means to justify their existence. Even if a lot was taken from them, they could still be secure in who they are and act as an independent will in the universe, regardless of what answers they did or did not have.
I have a rather good life. I have an amazing family. There's nothing inherently wrong with me. But I often look at people that have it so much worse than I do and I have to wonder how they make it through. Where does their motivation stem from? Can people really just live life without even feeling a need to question their existence?
I wish I had answers to that question. People are very complex and situations are as well, so one particular "solution" might or might not work for a particular individual at a particular time.
A lot of time religion obviously plays a role in coping. You see religion offering stability and security to people in unstable environments, so when everything else is going poorly they still believe that things will be okay and thus they endure.
But it's not even that clear-cut. You get things like Jewish people singing about their belief in God as they are marched off to the gas chambers to die while oily soot and smoke chokes the air: How does that work? And how does it work when the same Jews would both voice belief in God and act as if God exists even when at the same time they could decry God and claim he doesn't exist because He did not act? Even faith is not necessarily just a denial mechanism, it is a very complicated thing.
I think some types of people have it easier. For example, ESFPs seem less worried about the existential questions (except as fleeting party topics of conversation); as long as they feel they have some power, can do something that makes them happy, and have people around, they seem to cope just fine. But the people who are introverted, who live "in their heads," usually need more philosophical meaning invested in their lives.
Anyway, I might be veering off. I think self-contentment exists independently of life circumstance. You seem to be asking "how or why does it exist"? People seem to like to talk about that, and the topic shows up in religious circles a lot.