Trains were too fast to safely hand off bags of mail between train stations and trains while the trains were in motion, so instead they had to stop the trains entirely, which was slower than before. (I'm not sure why they couldn't just slow down the trains; maybe it was more a combination of higher speeds and changing priorities).

These were just special coaches added to high speed express trains. So the system was interconnected to the system of HS passenger trains as a shared infrastructure.

Ok so high speed passenger service was slowed to make mail transfer safe?

I’m still having trouble figuring out how speeding up trains delayed mail service. Was it just a scheduling issue?

The network is an interconnected system relying on average speeds and throughput. Slowing down or adding halts for the safety of a particular service probably wasn't an option. Hence the end of service. (The speed of that particular service consequentially dropped back to stationary infrastructure and transit between those hubs, roughly what it had been before 1838.)

I think I’m getting it now. When high speed passenger service ran at 50mph it could also carry mail and deliver 8 times a day. When passenger service increased to 75mph it was too dangerous to carry mail the same way so mail service dropped back to once a day, probably on dedicated or slower trains.