With 3-4 children, it sounds like the total survivor benefits were limited by the "family maximum".
The benefit amount the children receive was based on the father's earnings. The more he paid into Social Security, the greater survivor benefits will be. However, there is a limit to the amount of money that can be paid each month to a family. The limit is normally referred to as the "family maximum." This limit varies, but it is generally between 150 and 180 percent of the deceased's benefit amount. If the sum of the benefits payable to the children is greater than this limit, each of you will receive a benefit amount that is proportionately reduced.
As survivors "graduate" (stop receiving) survivor benefits, the TOTAL paid to ALL the children may drop, but the INDIVIDUAL amount paid to EACH child may rise as total payments fall under the family maximum.
A widow may receive full survivor benefits at full retirement age, or reduced benefits as early as age 60. A disabled widow may receive survivor benefits as early as age 50.
You may want to see here to learn about the appeals process. You may also wish to seek outside advice such as legal assistance.
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