Death of Female Zebra Finches

Question
I purchased a male and female zebra finch from a local pet store in July. The female had her 1st clutch in August but none hatched.  We removed the eggs from the nest and in September she had the 2nd clutch again none hatched.  A month later she died suddenly. Living 3 months.  We purchased another female a few days later. This female had her first clutch November 5th, she laid 4 eggs, 3 hatched, 1 was kicked out of the nest 3 days after we heard them chirp.  The two remaining survived and are doing fine. On 12/16 the babies fledged and on 12/26 we noticed 3 new eggs. We removed the eggs as to not tax the female. 1/1 we moved the babies to their own cage and they are doing fine. on 1/7 we noticed the female had plucked out all her tail feathers and there was an egg at the bottom of the cage. within less than 24 hours she became ill and died.  When she died she did have some discharge come from her eyes.  The male is fine.  Again we lost our female within 3 months.  We are afraid we are doing something wrong and it looks like our babies are 1 male and 1 female.  I plan on removing the female and putting her in her own cage soon.  They are 8 weeks old and I've read will try to mate as early as 10 weeks which we don't want to happen.  What can we do to protect our little female baby?  We feed them fortified food, frozen green beans, hard boiled eggs, crushed egg shells that have been microwaved to kill bacteria, vitamins in their spring water, clean them weekly, change their food daily...we're at a loss.  Please help.

Answer
It sounds like she died of wind eggs. Wind eggs are a result from the female's lack of calcium. The shell for the egg doesn't form or doesn't form properly and makes it difficult to impossible for the female to pass the egg. Crushed egg shells are an excellent start but lack the calcium that breeding females need. The website provided has a list of supplements you add to their food or water. The lady that owns the site is also highly knowledgeable about her products and can answer any question you have about them.
Note: While supplements are good for your birds, using them everyday can be dangerous. For supplements that are added to the water, one day of regular water after the supplements is vital so as not to give the birds too much of a good thing.
Wind eggs are unfortunately common; females will pull out all their tail feathers in an effort to get the egg to pass and become very lethargic. If in the future, you have a female trying to pass a wind egg there are somethings you can do to help:
Wrap her up in a towel and keep her warm
Keep her well hydrated (a syringe with the needle removed is perfect)
Keep her in a quiet area free of any and all stress

There is no guarantee that this will work 100% of the time but it does increase of the odds of the female's survival