2006 Accord will not crank
 

I am having a problem with my 2006 accord 4 cylinder/ automatic with 130000
miles. For about 6 months, once or twice a month cranking would grow slower and eventually the car would not crank. But waiting one minute or so, would crank the car at full speed and all was well for a few weeks. During this period the battery was replaced twice with no help. The car eventually hit a point to where it would not crank and would not recover after a few minutes. Starter made a sound where it sounded as though power was reaching the starter. Starter was replaced and the car started great about 6 times that day. After sitting overnight, same issue, no crank. Has anyone had this problem, and if so what was the remedy? Thank you.