It's not that the Big Bang isn't the presiding theory, it's that the Big Bang theory is an observational theory rather than an explanatory theory. That is, it's a model of WHAT we see when we look into space with our telescopes, not WHY we see it. That observation hasn't changed in 60 years - everything we've seen only confirms that the Big Bang happened.

What you're talking about was noticed pretty much as soon as the Big Bang itself was discovered. Basically the observed behavior of the early universe's expansion doesn't follow the known laws of physics as we understand them. The basic analogy is that the Big Bang should have exploded like a grenade, but instead it inflated like a balloon. This obviously had major consequences for the composition of our current universe, and scientists would certainly like to understand why things played out like this. So either our understanding of physics is flawed in some way (almost certainly true, but how specifically?), or something happened during The Big Bang to constrain expansion that we have yet to identify. It could also be a combination of the two.

It's one of the great mysteries cosmology is trying to solve. No matter what happens we'll eventually get a new theory that encompasses the Big Bang plus explains why it happened. The Big Bang itself will always be a good model for what it actually describes, just like Newton's Laws of Motion are still good models for specific scenarios of Einstein's Relativity.

It’s still the accepted theory among the majority of astronomers & physicists. Some of the big questions that remain are dark energy and dark matter