This is not remotely the case. E-book sales aren't declining. E-book sales percentage growth is declining. These are two very, very different things.
The 6.2% rise in book sales in 2012 were propelled to an increase by e-book sales, and in fact, e-book sales for children's books more than doubled. E-book sales were up 41% in 2012. This is less in percentage terms than the exponential 100%+ growth that was seen in previous years, but it still represents a significant rise in sales.
What is misleading about fixating on percentage growth is that it's looking at a market that started at zero five years ago.
Take these stats from the AAP:
E-book sales increase 41% in 2012
E-book sales increase 117% in 2011
E-book sales increase 164% in 2010
Seems like things are really slowing down right?
Let's look at those numbers again in real terms:
E-book sales in 2012: $1.3 billion (+$330.1 million)
E-book sales in 2011: $969.9 million (+$528.6 million)
E-book sales in 2010: $441.3 million (+$274.4 million)
E-book sales in 2009: $166.9 million
Yes, 2011 was a huge increase. But growth in 2012 (41%) was still greater than in 2010, when it represented a 164% increase.
Here's what that looks like in chart form:
UPDATE: As David Gaughran notes in the comments, the AAP's stats don't count self-published e-books, which could account for as many as 25% of all e-book sales.