"I'm wondering the position in the miner of the modules with the die #0 issue."
All of them came with this issue. 4 broken boards in the Jupiter and 2 in each Saturn I own. Of course, KNC offered to RMA all 8 boards, but I passed so far because of the 0.98.1 beta FW that managed to make my Jupiter and one of the Saturns work with all dies on, while the other Saturn was a bit more difficult to keep stable at high temps, but still got periods of time with all 8 dies on, sometimes 7 and sometimes 6. Unfortunately, something happened after I used 0.99 on my Saturns, one of them has a complete dead ASIC showing all 48 cores off (bfgminer doesn't even shows that module), the other starts with all cores on, but also turns them all off after a while. That's only happening on 0.98.1 beta or 0.98.1 official or 0.99. Both machines runs "normally" with die #0 off on 0.98 though. Weird enough, 0.99 didn't affect my Jupiter though, which was happily hashing with all dies on (and most of the cores) until today, when somehow it turned all die #0 off, but I switched to 0.98.1 beta and after the usual 1h heating up modules, it now hashes again with all dies on.
Failures that pervasive I'd suspect your power supply choice and/or noise on your AC line. But still, to be comprehensive I'd take one of your Saturns, reduce it to a single module that runs perfectly, then swap that out for all the other modules labeling each and characterizing each. The records would help I would think.
And don't move the ribbon cable with the module nor the blue power cable, stick with those that produce the 100% functional "Mercury" of one of your Saturns.