Is it possible for virus infected cells to continue to present a self-antigen on the MHC1?
Self antigen is presented throughout viral infections.  You seem to think that cytotoxic T lymphocytes respond to absence of self. That’s backward. CTL respond to their specific peptide target no matter how much self antigen there is. In a typical response, there may be 100,000 self peptide/MHC complexes and 100 viral peptide/MHC complexes, and that’s enough for a CTL response. 

One trigger for NK cells is absence of self, so perhaps that’s the source of your confusion.