The NY Times website can be very aggressive with regard to making sure you only get so many free articles per month. I've found the most reliable way to bypass their restriction is to always view the site in privacy mode so they can't leave any trackers on my computer. Otherwise I sometimes click a link to find "you have already viewed your ten free articles for the month."

Your mileage may vary, of course. It's my recommendation to avoid having trouble with the site.