Why do people talk about the decline of American power? Where is the evidence?

[Sevengen]

additionally, throughout history, a nation's military might, or power as you're referring to in the OP, is a reflection of and direct extension of it's economic power. While these two aspects of a nation's overall health and world influence do not rise and fall in exact proportion to one another, they are fundamentally tied together and do, over time, exhibit direct consequences on each other.
This link:

http://www.newser.com/article/d9pjkt4o0/us-falls-to-5th-slot-in-economic-competitiveness-survey-swiss-stay-on-top.html

is to a recent article concerning America's economy in relation to other countries. As our economic competitiveness wanes, so will our influence, i.e., respect, perception among other leading nations.. and eventually, our military might.