As many have said, a lot of people give up because of one or more of the following:
-they feel like they don't improve
-they are disappointed that their art gets little attention
-they don't enjoy it
-they don't have the time and must make sacrifices
-they get discouraged upon seeing better artists
-they are impatient
I have never wanted to give up art, but I did want to give up posting it at one point. When all of my friends(in real life, might I add) got many more watchers on DA than I did, I got heavily discouraged. I kept going though. I want to say this story has a happy ending, but I never surpassed either of them in watcher count, which was a mere 100 watchers over the span of two years. I ended up quitting DA though not because I wasn't getting results(I got over that) but rather because my parents condemn it because they believe it had bad influences on me(I was in a bad headspace but they blamed it on the attention seekers there even though that was not the case.)
Whenever I feel discouraged about my art or feel like I don't improve(such as the fact that my twelve year-old cousin became a high quality artist in merely a YEAR), I look back on my older stuff or even redraw an old piece. It gives me reassurance that I have gotten better. As my talented artist cousin once told me, "you'll never get as good as you want to, but practice will make your art improve." So I don't give up. After all, I have plans to be an animator sometime in the future and that will be a very difficult task, so I can't give up.