This is a difficult question, because there are many theories of why the Roman Empire fell. In my opinion, the most cogent reason for the fall of the Roman Empire is that Rome imploded on account of its sheer complexities. In other words, the Roman Empire was too vast and too complex. So, Rome self-imploded.
If we take this to be the main reason for the fall of Rome, we can say that there are many good parallels to American today.
First, America's interests are vast. Therefore, there is an argument to be made that America is overreaching. For example, America is involved in almost every part of the world. There is no way America can be successful in all of these theaters.
Second, the world is growing increasingly complex. If we think of the banking sector for a moment, not too many people know what is going on from an economic point of view. The collapse of the banking sector of 2008 is proof. The next collapse can be even greater.
In light of these two points, it is possible that America will lose more influence on the world stage. As it does, the power of America will decline or even fall.