Yes, the bottom first true leaves often die prematurely, however they are very easily burnt too. You do not say in your diary if you are feeding it anything, but if you are, a plant that size/age needs very little feeding. About 20% of what it says on the bottle and only once every 7-10 days or so, after it has grown her firs 4 sets of leaves roughly. Also, your substrate also looks rather wet, again, a plant that size/age needs only moist soil and watering every 2-4 days depending on temps. At this stage I wouldn't be worried about what is going on, she will pick up as she grows. Just resist the temptation to feed it too much or water it every day. Your plant is still a baby trying to figure out what life is all about, and doesn't need lots of water and a T-Bone steak quite yet. Just like a human baby, it needs gentle feeding and watering, in little amounts.
Hope this helps,.... Organoman.