I can't really think of a game I never beat due to difficulty. But I can recall one in particular that I did beat, but was at the breaking point of giving up on. The name of the the game is King Arthur's World for Super Nintendo.
I was about 12 or so when I played it, and I remember you had to quickly manage a team of archers, knights and engineers for example. It's by far the hardest game I can remember playing. In short, really difficult game to beat especially for a kid, that just got progressively harder. And the save point system sucked. I spent hours upon hours trying to beat it.