Hello abeille, I grow some sedums and from what I have seen with them, it undergoes that cycle of drying out older lower leaves as seasons change from warm to cold. I grow mine outdoors, and they love our mild winter conditions here. But I do grow them in a very gritty media, since we got more rains in winter. Then come the arrival of Springtime, it will undergo another cycle of that leaf drop, it is its way of adjustment. When the sedums starts to show that much stem in Spring, that is the time I cut it off, dry out the cutting and root it back into the media. They go somewhat dormant here during our extremely dry and hot months and resumes active growing when cooler conditions return.
With your plant, more watering is not the answer, keep your media more draining and grittier. Protect the base of your plant, if you can add some pumice, crushed granite (chicken grit) or mix in more perlite. As long as that stem remains firm and green, there is a chance, that it may still grow new leaves at each of those nodes, but typically new growth is often from the center tip.
