You aren't replacing your components before they break and make the car inoperable, thus, a qualifying time of 0:00.00 and on the track you break down.
When practice and preparing in the next race tab you have to make sure you have enough mechanics and engineers to replace the components that need replacing in the Assembly tab, between the Info and Driver set up tabs.
Make sure you have 34 engineers and 24 mechanics to be able to fully replace each and every component on the car in one time if need be. This may not be possible since you do not yet have the maximum available staff size, but until then you need to replace any components that are close to breaking, aka 0% condition.