Sure, every Go player hits a plateau in their playing career, in fact more than one.

As a proto-Go player (and I think of myself as a dabbler still), I used to have a specific computer program as my sole opponent: IgoWin, a tiny 9x9 Go program which I still think makes a pretty good introduction to the game.

When you start out as a total beginner IgoWin gives you 5 handicap stones, which on a 9x9 board makes for a real easy games. Then, as is traditional, every time you win a game it takes away one handicap stone, until the games start to become challenging again.

My first ever plateau in learning Go was when I got IgoWin to play me even, taking Black. As White I was totally unable to beat it. No matter how much I played (for weeks on end) I couldn't figure out how to get past that.

After a while I broke down and asked a friend of mine who I knew was a player to teach me the basics. Two or three games with him on a 13x13 board later, I was able to clobber IgoWin as White in even games. I started playing human opponents exclusively, and later learned that bots like IgoWin are considered a bad way to learn, because Go playing programs so lack an understanding of the game that playing them will give you bad habits.

So the idea is that there are plateaus, but there are also plateau-busters. For me, playing with a "real" opponent who knew what he was doing was one. Another was reading in-depth reviews of games at the GTL. Yet another was to do lots of tsumego from graded problems books. Also, reading important books like In the Beginning or Attack and Defence, which help make sense of the whole game and give you a conceptual framework in which to plan your moves.