On some phones , when power saving mode is enabled , it also deactivates network connection ( 3G/4G/5G ) . However , it might be the case that somehow your phone goes into flight mode / airplane mode ....
Need more info.... Before you enter your car everything is fine ? How about when you leave the car ? Everything goes back to normal ? When in the car , and you say your phone goes offline , how exactly do you realise it went offline ? Does the car notify you or the phone ?