Although I made a specific thread on it, do you guys find S. Repens struggling to take hold of the substrate? I use Fluval Stratum and I had about 20 stems planted a month ago and still have to replant the majority of it after 1 month! - the little that does grow, grows slowly in a 30-40 PAR (at substrate) tank with EI and injected CO2. Most of it has subsequently withered after never grabbing hold of the substrate and I had to throw it out. I'm left with maybe 10 stems.
I too noticed some of the same rot and promptly discarded the affected stems. Since I still can't get a proper carpet going, the rot probably didn't have a chance to propagate (if it indeed does).
But that sort of propagation has to be something localized...either a secretion or added chemical or some sort of bacterial/fungal rot. Although I'm not a botanist, I can't imagine that's a normal part of S. Repen's growth cycle.
I believe your lighting might have something to do with your problem, although I've grown mine in even lower lights, were they emersed grown prior to you planting?
However I've never seen the rot that this thread is focused on, the most issues I've seen from this plant is when they choke each other for light.
Also I'd add they plant is very nutrient demanding, within a week it would show deficiencies if not dosed.
Another tip would be the same as all the other online sources, the longer the bare stem planting the better, I've always they rooted much better this way.
This picture shows my stauros roughly a month and a half after planting, they were immersed prior so that took little adjustment, but had almost 2-3" roots within weeks, they seem to really do well with root tabs.