We have a well accepted theory to explain the glacial-interglacial cycles during the Quaternary Ice Age. My question is, why did the Earth enter the ice age gradually?
this is really interesting question and certailny debatable issue. I am not in a position to answer it or discuss in details but please see one of the questions asked on RG by Victor Christiano about global cooling and/or warming. Have you seen it already?
The most simple answer is because it takes longer to accumulate ice than it takes to melt it. Ice accumulation can only be as fast as the winter snowfall. The ice sheets that existed during the glacial were several km thick. To build up this much ice, you need a long time. The melting and disintegration is fast, completed in less than 10,000 years.
It looks to me like you are asking about the onset of the Quaternary glaciations in general, in which case I recommend you read Cane and Molnar (2001) (http://rainbow.ldgo.columbia.edu/papers/canemolnar.pdf). They concluded that the change resulted from diversion of West Pacific Warm Pool water following uplift of Halmahera. I think they are correct that the closure of the Indonesian Gateway was critical but their detailed model is inconsistent with Karas et al. (2009) (http://www.nature.com/ngeo/journal/v2/n6/full/ngeo520.html). The timing and nature of events recorded by Karas is more consistent with a change caused by the uplift of Timor in the Banda Arc, which caused major changes in the regional oceanography.