That is a typical underpowered PC problem, that the computer is not powerful enough, because on software startup and on file load the software eats up a bit more power than otherwise when in idle and when executing g-code.
So, if the connection is lost on software startup or on file loads then it is a problem with the computer power, it is on the edge of what is enough/not enough for the UCCNC...
Yes, the machine stops milling if the connection losts. The motion controller in that case stops generating the signals for the drives and puts the hardware signals to their default off state, e.g. the spindle relay output to it's configured off state etc.