We don't have to go back very far for a good historical example. Think of the previous recession which puts this one to shame, Rolls Royce et al didn't change their prices one cent. From memory neither did Specialized, Pinarello.
Their strategy is usually to focus on adding a new shiny model (ergo, new Veblen good) to entice the target market which responds to such stimuli. In the cycling market, where most brands have clear stratification of different models, they're also betting on lowering the price for entry-level models to increase cash flow and flush out stock. But, again, a cataclysm would have to ensue for us to see S-Works and Dogmas with lower RRPs.
Of course this isn't 100% impervious to variables and confounders. In that same recession, many of the very rich had a bunch of their portfolio tied in real estate. Those surely tightened their belts and I'm sure demand took a hit. But that means nothing on the supply end. They won't panic and won't cut of the nose to spite the face.