Demonkin, you can't astral project while in a lucid dream. If trying so, you will either wake up or change your surroundings of what you perceive astral as. And it's a great way to land in sleep paralysis, which can be a horrid experience for beginners.
The silver cord is simply what connects you to your physical body and astral body. It can't ever break but can become weak. I think you're becoming too relaxed. It sounds like you may start falling asleep, but sleep apnea may be a problem. Or it may simply be an illusion. Nevertheless, if this carries into regular sleep, consider medical assistance. Otherwise, change positions. Sometimes unusual positions land you into comfortable trances and will provide a safe passage into the astral world. Make sure you aren't strained or uncomfortable whatsoever, or your experience will be unpleasant.