I would recommend replacing the entire wiring harness from the ceiling to the fixture.

For a temporary repair, you might use heat shrinkable tubing. Stagger the connections so that they are not next to each other. I emphasize that this should not be used as a substitute for properly replacing the failed part (the wiring harness).

Did someone by any chance fit lamps to these fixtures that are of higher wattage than the manufacturer recommended?

Thank you.

They are using the correct bulbs (T4 G9 halogens, 60 watt). Unfortunately, reaching the ceiling to replace the entire wiring harness/cord would require a ladder contraption that I am not familiar with.

I still wonder how they were installed, since they're 3' beyond the 2nd floor landing rail (with 10 ceiling up there) (over a wide kitchen island on the first floor, 10' ceiling down there), yet about 7' off the outside wall so a ladder would be a problem.

If there continues to be an issue, would it be advisable to raise all the pendants (cut some wire), and install lower wattage sockets and lamps (bulbs) on freshly stripped wire? Just a thought for down the road, in leau of replacing everything with an acrobat/mountain climber.

How close is the joint to the fixture? Solder could melt if it becomes too hot. Crimps might vbe a better solution.
To cover the soldered joint I would use heat shrink tubing. You slide it over the joint and heat it. It shrinks tight over the wires.

Thanks. The joint is close, meaning no more than 2" above the socket, and the socket is screwed to a part that holds the shade in place. BTW, wouldn't the heat shrink tubing melt if it's that close?