I suppose it also comes down to how you define a big game.
I would say that the 5-1 demolition of Cardiff at the back end of the 1970-1 season was an emphatic win in what was a very big game in the context of that season. And we followed it up with a 3-0 win against Watford. Also a big game in the context of that season. 42,963 and 38,857 turned out for those matches which tells you how 'big' we thought they were
At a lower level, the 4-0 win away at Peterborough in the fourth division season was of huge importance.
And, of course, there was the 5-2 away win at Leicester which confirmed our return to the first division after a 14 year absence. At that time it was the longest period of time that either Sheffield club had been absent from the top flight. At the start of play we were just 2 points ahead of Newcastle and with a worse goal difference. We had to win to be sure. That was a huge game.
But I take your point, that there have been far too many occasions where we have come up short in big games. But, we do succeed occasionally.