I became interested in this case because the age enhanced picture of Anna looks very similar to one of my friends. Though my friend was born in 1962 and was legally adopted as an infant....Anyway once I started I couldn't stop reading.
After reading for several hours and viewing the pictures of the farm Anna became missing at, my very first thought was she fell into an abandoned well. With all the rain at the time, a formerly insufficiently capped well could have become weaken. If the child fell through, a pooling effect of dirt/mud could have recovered the hole to appear as just another mud puddle.
We moved to an old farmstead in NE when we first got married, and capped an abandoned well when we had our first child. Years later we received a letter from the State of Nebraska with a "Platte map" of our farm showing
THREE other abandon wells on our immediate property that we never knew existed. After careful examination we located them, and capped them, but one was so disguised by brush and tall grass that we would have never noticed it until it was to late.
I have read numerous stories over the years of children as well as Adults falling into abandon wells. In one story a grown woman was knocked out cold for several hours from the fall until she regained conscience. It was still 2 days before she was found alive.
Hopefully this scenario has already been checked out over the years but it could be a highly probable answer. Living in a farming community with a history of raising livestock (Various wells for stock water tanks) this is a fear of many country parents in my area.
The following is a link I found describing the dangers...though it's a MO site, the facts remain the same for any state.
http://www.dnr.mo.gov/env/wpp/wellhd/plugging.htm
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DEADLY TRAPS
Abandoned, large-diameter dug wells and cisterns are a very real and deadly threat to the residents of rural Missouri. If kept in good repair, they present little threat to human safety, but many well and cistern covers were constructed from wood that can be weakened or destroyed by the elements. Even concrete covers are subject to deterioration. In recent years, abandoned wells have received much notoriety in the press when they have claimed the lives of children who have fallen into them and drowned. Many dug wells and cisterns are still in use. When properly maintained they present little risk, but when abandoned they become potential traps and are an unnecessary risk to human
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Hopefully for the sake of Anna and her obviously loving family this is not the case. My prayers are with you on your search.