All 'models' predicting the technological singularity are based upon, they require continual exponential growth - of intelligence, of technology, etc.
Well, if history showed anything, it showed that exponential growth in anything other than abstract mathematics is not sustainable - regardless of your attempts to 'cheat' this rule.
Technology matures and can't be improved further; etc.
Yes. Real-life processes aren't simple mathematical curves; there are many factors that interact and affect one another, and eventually any short-term trend is going to slow or stop or even be reversed. Generally, the norm is equilibrium; rapid change occurs when the circumstances are right and there's a need or incentive for it, but eventually a new equilibrium will be reached and things will stabilize again.
Sure, computers are transforming our lives in ways our forebears couldn't predict, and that might continue. Eventually we may have computers so advanced that they can precisely model and predict things like weather, natural disasters, economic patterns, social and psychological dysfunctions, etc. and give us reliable mechanisms for avoiding problems and disasters before they happen, bringing a new age of peace and security and prosperity to all. And they may bring new breakthroughs in physics and technology that will let us expand into space and improve our standard of living and restore the Earth's ecosystem. But the people who enjoy it will probably not be any more fundamentally intelligent than we are. Will they have more immediate access to any information they need? Sure, and they'll be able to draw on the problem-solving ability of the rest of humanity through crowdsourcing as well as that of the superfast computers. But they'll still probably think on much the same level that we do. And there's no guarantee that the computers will be any more intelligent, just faster and more powerful.