Well, I'm no electrician so my comments must be taken with caution, BUT the consensus of opinion seems to be that a major part of the problem centres around the resistance across the connection block in your picture.
It may be borderline ok when in perfect condition but the slightest deterioration due to eg corrosion or moisture increases its resistance to the point where it overheats ... at which point it deteriorates further and rapidly until it burns out.
Now, as I said, I'm no electrician but I can relay my own experience, as follows.
Shortly after I bought my M750, with only a couple of thousand miles on the clock, I was caught in a torrential downpour on my way to Brands Hatch for a BSB meeting. This would be about 2005 ish.
On returning to the bike after the racing, I found battery acid (from the liquid filled 16ALA2 battery) dribbled all down the left side of the bike, with damage to the paintwork on both the frame and the alternator cover.
Surprisingly, the bike managed the return journey home with no obvious issues and, perhaps foolishly, I replaced the missing battery overflow tube, repainted the alternator cover and thought little more about it.
Not long after that I was riding locally and pulled up at a tee junction, blipped the throttle (for no real reason) while waiting to pull out and heard metallic pinging noises coming from under the petrol tank.
I pulled over to the side of the road and lifted the tank to find four of the six battery filler caps had blown off the battery, which had boiled itself almost completely dry.
I replaced the caps which, luckily, were at the bottom of the battery tray and again, unbelievably, the bike limped the couple of miles home at low revs.
On inspection, the connector which you have pictured was corroded and a little burned and (again, somewhat stupidly) I cleaned it up and refilled the battery and found that everything worked well enough to enable me to properly test the charging system.
These tests pointed to a failed reg/rec so I replaced it with an Electrex unit, but continued to use the old connection block, which only showed minor damage .. the sort that you could just about say was cosmetic only.
A couple of weeks later, on a short trip just a mile down the road to the stainless bolts shop, I could smell burning. The bike was reluctant to start after coming out of the shop but eventually it fired up and it rode home ok (just a mile or so).
On inspection, the connector block was totally melted.
At this point I decided to hardwire the alternator connections (three yellow wires) using homemade copper crimps covered in glue-lined shrinkwrap tubing. I also rerouted the wires so that I could get my hand to the new crimped and sealed connectors to feel for any heat in them.
I never felt any overheating.
By now the bike had covered about 5000 miles at a rough guess.
Since then I have covered a further 30,000 miles, without the slightest sign of a problem. Possibly 20,000 of those miles have been with a lithium (LiFePO4) battery fitted, still using the Electrex reg/rec (ie without replacing it with the Shindengen upgrade which is often recommended).
It has been totally fine all that time (including a few wet rides, notably the biblical downpour we rode through while crossing Dartmoor on the Coast-to-Coast run some years back).
Like I said twice before, I'm no electrician but all that seems to me to point pretty conclusively to the issue being the unsuitability of the cheapo connection block which Ducati fitted as original equipment.
Hardwiring seems to cure it but if you would prefer a removeable connection block then my notes from back then list a "Delphi Metri-Pack 630 series" sealed connector rated at 46amps which I was considering fitting. These used to be available from "Kojaykat" but I think they may have since gone out of business. There will surely be an alternative supplier though.
But the crimped and sealed hardwiring has worked fine for me so I've not bothered going further.
Gazza will probably recommend gold crimp connectors, but I've not found them to be necessary.
I made my copper crimps by rolling thin copper sheet around the shank of a small drill bit. Two wraps makes a tidy crimp which withstands the squeezing nicely.
Using such (naked) crimps means you can crimp them up and then cover with undamaged shrinkwrap, rather than the one piece covered crimps where the act of crimping damages the shrinkwrap outer.
I avoided soldering because such connections can often fail at the point where the stiff soldered portion meets the flexible unsoldered strands .. and also perhaps due to concern that any flux residue would cause future corrosion.
The glue-lined shrinkwrap not only seals out the moisture but also supports the joint off the insulation covering.
Like Rob said ... while I was typing this.
ps. I don't think its possible to get the three wires the wrong way round.
Better electricians than myself will hopefully confirm.
Replace the white connector with three separate bullet connectors. Isolate them well from each other.
