I've never felt a need to pick up tickets at any point other than the day of departure. I just use the Quik-Trak machine to print the tickets, then hop on board. Plus, if you ever need to cancel at the last minute, it's free and easy. NPN is staffed, so if there's any problem they'll be able to help you out.
The only time I ever had a problem was when I was going CRT-Toronto on the Maple Leaf. I was traveling with my father, who had never stepped foot on an Amtrak train before (and couldn't remember if he had ever been on a train pre-Amtrak) and was hoping to create a very good impression of rail travel.
We arrived at the station early, went in, and approached the Quik-Trak machine (there is no Amtrak agent at CRT, just a machine). I used it to pull up our reservation and then it began printing our tickets. Or at least it tried to. It ended up not giving us anything and switching to an out of service message. I immediately called Amtrak, and was told to explain the situation to the conductor, and that we would have to ride to Albany, where we would have to run into the station quickly and repurchase our tickets from scratch, at our own expense. Then we'd have to send the ticket stubs to Amtrak for reimbursement. Needless to say, this was not how I wanted the trip to start! My father handled it very well, though, and we got on board and explained the situation to the conductor. He told us he'd make a call and get back to us. A few stops down the line, he jumped off the train, ran into the station, and then ran back. He promptly showed up at our seats with our original tickets which he had the station print for us before the train arrived, which was a very nice surprise! My father was very pleased and it set the tone for a wonderful rest of the trip.
