At least not according to Google.
Dan Friedman, Product Marketing Manager, said:
“Google does not keep track of your landing page Quality Score history. We've heard some concern from advertisers who think their current Quality Score is being lowered by previous landing pages' Quality Scores. However, Google only uses the most recent check of your landing page to determine its relevance and quality.”
VKI note: Landing pages are just part of quality score; you should take a holistic view of quality score. Learn more about how Google calculates Quality Score.