Not for just a delay. However if you have booked multiple trains with guaranteed connections i.e. all booked on the same reservations, Amtrak will compensate you if for example you booked a sleeper on a connecting train and due to your initial train being late you miss the connection and had to stay over for the next days train (they will provide hotel and meal vouchers in this case), and the next days trains had no available sleepers and you had to ride coach, they would compensate you for the difference. In some cases you might get compensated for other downgrades e.g. no dining car available and you were in first class (sleeper). You would likely have to contact Customer Relations, they probably wouldn't volunteer this.
Because most Amtrak trains outside of the Northeast Corridor operate on freight railroad trackage they are at the mercy of the Freight RR dispatching which can vary, some RRs are better than others about giving passenger trains priority. Plus there are the usual breakdowns, level crossing incidents, trespasser strikes (since we don't fence off most of our rights of way unlike the UK) and so on. One takes Amtrak with the expectation that one will probably be late, especially long distance trains.