Did you know that Amtrak will also reimburse you if a train is significantly late, you spend the entire trip with a kid kicking the back of your seat and the attendant won't let you move, etc.? All you have to do is call and ask for it. The standard rules for dealing with customer/tech support apply... BE NICE, understand that they are not REQUIRED to do anything particularly amazing for you but do have the OPTION to, etc.
I don't know if 30 minutes qualifies, but I can tell you I've gotten vouchers for the full amount of my fare, sleeper cost included, for a train that was a couple hours late. And I've gotten partial-fare vouchers more than once as well. See http://www.amtrak.com/about/satisfaction.html
In terms of customer service, within the past couple years, I've had MUCH, MUCH better luck with Amtrak than with airlines.
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I don't know if 30 minutes qualifies, but I can tell you I've gotten vouchers for the full amount of my fare, sleeper cost included, for a train that was a couple hours late. And I've gotten partial-fare vouchers more than once as well. See http://www.amtrak.com/about/satisfaction.html
In terms of customer service, within the past couple years, I've had MUCH, MUCH better luck with Amtrak than with airlines.