J-M-L:
There is no extra Resistor or diode in your jack setup ?
There was not, initially, but I installed a 10k resistor on the A0 input from the jack yesterday evening.
And this morning, both system's clocks reset again... With the new code and the extra resistor. 
There must be another flaw...
[EDIT]
I also noticed that, when the hour at which the system is supposed to allow the opening when a jack is inserted (7AM) is reached, it doesn't... until I open a serial monitor console, and then it refreshes the time and system is up. It's as if time was "frozen" outside of the opening hours (7-22). When I open a console before 7AM, time shows every 500ms, as programmed, but the time reading stays the same (whereas before it did change)...
[EDIT2]
I've decided to take the RTC out of the equation by using a programmable power socket instead, that will turn the whole Arduino & electric strike on and off, with a simple code running. This is a bid disapointing but this is an emergency call... 