The NYT's digital subscriptions have been increasing steadily for quite some time [1], and while their print subscription has fallen by approximately half since 2001 [2][3], they have more digital subscribers now (2.5 million) [4] then they had papers in circulation in 2001 (1.1 million for the weekly, 1.7 million for Sunday) [2].
That doesn't seem to suggest that the NYT has lost trust from all of its readers, to be honest.