Rome - Shanghai - Ho Chi Minh and then Ho Chi Minh - Shanghai - Frankfurt

Hi, I was just wondering if we will be eligible for the 72 hour visa-free stay both times.

We are leaving from Rome to Shanghai (3 days) then to Ho Chi Minh (1 month) and then we will be going from Ho Chi Minh to Shanghai (3 days) to Frankfurt. I was wondering if logically we will be qualified for the visa-free stay on both times we transit to Shanghai as we will be arriving and going onto different countries. We are from the UK and travelling all legs with the same airline.

Thanks in advance.
Kha