Actually, you've got two issues to address here.
As the other responses indicate, setting InDesign's View>Display Performance preference to High Quality Display with no documents open within the program, immediately closing down the program and re-opening it will set all new documents with your desired preferences.
But you have to do that drill for existing files, and ones created by others, because your display performance is a document-level preference. Any previously-created documents which were created and saved with other display preferences will keep those preferences until they're changed — even if you've changed your default display preferences on your system. For those documents, you'll have to change the preference to what you desire and save them to get the results you're looking for. Each and every time. I suspect that's the issue behind your shifting display preference problems.
And alas, the only fix would be to change the existing document preferences on a file-by-file basis. If you're like me, while muttering and cursing under my breath that I have to do the whole drill again for each old file.
I know this doesn't help per se, but I suspect it is the root of your shifting preferences problem.
Randy