Why can GPS issues delay a train 45 minutes?

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The issue is almost never the wider GPS system (it's run by the US Space Force,) but rather something with the GPS receiver for the train or some interoperability or link specific to the setup used by the rail operator. There would be a lot more issues than just trains having to stop if the totality of GPS were to go down for any significant period of time.
Much more likely the data radio communications component on the fritz than the GPS. Every single PTC variant out there includes a locomotive data radio unit for communicating with wayside interface units located on wayside signal equipment as well as back office servers for downloading movement authorizations and other things like temporary speed restrictions. The I-ETMS system which is the one that uses GPS for positioning is a quite complex and dynamic system and involves a lot of radio communication.