Is it possible for virus infected cells to continue to present a self-antigen on the MHC1? Forgive my ignorance, as I'm new to immunology, however it seems like there would be some amount of positive selective pressure for viruses to develop the ability to continue to present the host's self-antigen on the MHC1 of a newly infected cell, thereby disguising the infection from the body's immune system (or at least from the cytotoxic T cells). Is this in theory possible? Or is there a reason it cannot occur.

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.