Looks like stem rot from keeping the soil right at the top too wet which is an all-too common problem at this stage of growth. Try mounding a little soil around the base of the plant to prop it up, and water away from this mound until the plant is sufficiently stronger at the base. Plus, you will get roots from any stem you bury but don't cover leaf nodes unless you snip off the leaves tight to the stem first. It also looks like they may be reaching for light but usually what you are experiencing is from too wet of soil early on when the stem is tender and soft and goes away when allowed to become more woody. Prop it up, let it dry around the base and water away from there for now. Once stem rot sets in, it is almost always fatal unless you can successfully prop the plant up and hopefully the stem grows and gets healthy again. As for jiffy peat pots, don't use them if you can help it. If you do, when you are ready for transplanting, carefully tear off the pot as roots really struggle to get through that stuff. If there are a few roots penetrating it already, no problem, you won't kill it by tearing off the pot as long as the root/soil mass is not broken apart. I doubt your roots have even reached the outside of a peat pot yet, judging by your pics. Before roots will break through a peat pot, they usually curl around inside it, making for a small plant until such time as you set it free of the peat pot and the roots have a chance to really spread out.