So I replaced my starter about 4 months ago because the original one was shot. Last month I was hook in up to my camper trailer and the truck wouldn't start just a solid click from the solenoid on the firewall. So I clean my battery terminals the were discusting. Truck started fine. Now this weekend the same thing happens. Always seems to happen when your in a hurry to go somewhere. I changed my terminals this weekend. I tried starting and it made the loud click then rrrrrr slowly cranked. Then it was good. Then I went out this morning on my way to work and it clicked so I cycled it 3-5 times and it finally completed the circuit and away she went.

 

When you installed the starter did you scrub the area where it makes contact with the tranny? Sounds like you have intermittent ground current. Also, The hot wire connection to the starter can break easilly where the blade is bent, it can seem like its still intact when its only conducting at about 20%.