When they do an "X-free articles per month" thing for a paywall, they usually set a cookie on your browser that keeps track of the number of times you've accessed the website that month, and bring up the paywall when they've detected you've reached the limit.
No-Script and similar blockers defeat the scripts that are used to implement this. Another way around it is to either use a private window, which bypasses cookies, or delete all cookies for that website whenever you hit the paywall.