kexec’ing takes a long time, and connections can timeout during that time. Try waiting longer, it’s probably actually running kexec still while the connexion drop. In my case I had to wait a bit longer than 5 minutes, but I guess if your instance is slower for whatever reason, it could easily take double or triple that.
Rebooting during kexec will always bring back the original Ubuntu, since kexec is an in-memory only thing. It’s only when you start doing destructive operations that this may not be true, i.e. in my blog post, when you start deleting the original partitions.