I am happy to report that the problem is resolved.
Contrary to what I had been told (don't remember who had told me that...) there is adjustment on these doors.
Lifting the doors slightly and loosening the hinges bolts made the doors aligh vertically. Then loosening and moving the latches about 1/16 inwards made the doors close tighter.
When I loosen the hinges bolts, I found that they were not very tight at all ! Not loose but you know, not a big effort was required for the bolts to begin turning. Probably the initial cause of the problem.
Thank you very much guys, your help is greatly appreciated