With myelodysplastic syndrome why does the body stop producing blood?

the blood is synthesized in the bone marrow of the long bones.
in MDS (Myelo-Dysplastic Syndrome), the bone marrow undergoes FIBROSIS i.e. replacement of blood elements with fibrous tissue that are not functional so the bone marrow does not produce blood any more.
As why the bone marrow become fibrosed, many theories, one of them is the megakaryoblast ( that is responsible for synthesis of platelets) will secret some factors that enhances the producton of collagen causing fibrosis.

known as Preleukemia
MDS is thought to arise from mutations in the multi-potent bone marrow stem cell, but the specific defects responsible for these diseases remain poorly understood. Differentiation of blood precursor cells is impaired, and there is a significant increase in levels of apoptosis in bone marrow cells. Clonal expansion of the abnormal cells results in the production of cells which have lost the ability to differentiate. The accumulation of these cells, called "blasts", further impairs the production of normal bone marrow products, If the overall percentage of bone marrow blasts rises over a particular cutoff (20% for WHO and 30% for FAB) then transformation to leukemia (specifically acute myelogenous leukemia or AML) has occurred. The progression of MDS to leukemia is a good example of the multi-step theory of carcinogenesis in which a series of mutations occur in an initially normal cell and transform it into a cancer cell
read more in Wikipedia

Actually Myelofibrosis is a process that is different and considered separate from Myelodysplastic Syndrome (or MDS). In MDS, the normal hematopoietic stem cells (cells that produce our other blood cells) becomes dysplastic, or abnormal/bad, and under the microscope, a bone marrow biopsy will reveal these cells predominate rather than normal looking stem cells. These cells proliferate and replace the bone marrow, and therefore the normal stem cells are displaced and the body stops producing normal blood cells. It may affect one blood cell line or all three (white cells, red cells, and platelets).

In more advanced cases, very abnormal and immature cells called blasts accumulate and when the number of blasts reach a certain percentage, a patient is considered to be in Acute Leukemia (AML, as the previous poster points out). The cutoff used to be 30%, but today, under the World Health Organization (WHO) classification, people with 20% blasts are considered to be leukemic.