Destroy gradually, erode; also, worry one constantly
Example 1: The sea has been eating away at the outer banks for years.
Example 2: The fact that he failed the test is eating away at him.
Example 3: In that time literally millions of bombs have rained down on the soft Holderness earth - and now they are all being exposed as the cliffs are eaten away by the sea.
Example 4: The stone blocks had been eaten away by time and now were only a shadow of their former glory.