I haven't had problems watching series I've bought but on the Prime Videos I was watching through NYPD Blue and when I got to the 5th season they removed it. The early seasons came back after a few months as paid videos but the season I was watching didn't.
That happened on Netflix once, too. I was watching the series Hack and I was in the second season when they removed it. I called and the support guy didn't know why but he checked and said it wasn't coming back. It hasn't.