What is the mechanisms responsible for downregulation or loss of MHC-1 expression on the surface of cancer cells？
There is no single mechanism (as you'd expect, since there is no evolutionary relationship between different individuals' cancers).  The most common mechanisms are various forms of mutations, ranging from point mutations in single MHC molecules to large deletions of the MHC locus. Mutations in genes involved in antigen processing, that are not themselves part of the the MHC locus (e.g. TAP, b2-microglobulin), are also fairly common.  Epigenetic changes are also not uncommon.  There are several reasonably recent reviews, including 


MHC Class I Antigen Processing and Presenting Machinery: Organization, Function, and Defects in Tumor Cells
Different regulation of MHC Class I antigen processing components in human tumors
The escape of cancer from T lymphocytes: immunoselection of MHC class I loss variants harboring structural-irreversible “hard” lesions