P0413 VOLKSWAGEN - after car warms up for extended period shuts off

Question

My step daughters beetle when is warmed up happened 2 times, left idling in garage (with door open) for approx 50 minutes the first time, then 25-30 second. Engine shut down. Heater and seat warmers were on. temperatures outside upper single digits to mid teens.
Today when it occured the P0413 - Secondary Air Injection System Switching Valve A Circuit Open code was thrown. I cleared it and is running fine now.
Question is can the idling cause this in cold temps with the 10% ethanol in gas these days?
They have been told to not warm it for more than 10 minutes in the future.

Also, after clearing the code drove it around on some errands no other issues.
thanks