thanks for the answer.
replacing the low-water shutoff circuit shouldn't be that difficult. As far as I can see, if there is current through RE and EB, than there is water in the well, if not, the pump must be stopped. All I need to know is the minimum value, under which I must shut off the pump.
The pump is turned on when the pressure switch is ON ( if no lack of water, indeed).
But I'll do that in several weeks, when I have time.
For now, I'm trying to figure out what causes this weird behaviour, which component is the culprit, and change it.
What makes it difficult is that it is a "random" breakdown, not reproducible .
Buying a whole replacement system would be too expensive for the house owner ( I'm only an occupant 
) .
And now, I'm frustrated, I need to understand
PS : Actually, I'm not "inexperienced", I studied and worked in electronics ... okay..... long time ago , and I've been working on PLC for several years. But sure, I need to practice and remember ..... 
edit : typo correction