iOS tries to be clever about when it allows an app to refresh itself. It takes into account…
- Whether the battery is nearly dead, and whether the phone is plugged in: it will refresh more frequently if the phone is fully charged or currently plugged in.
- Whether you're on wifi or the cell network: it will refresh more frequently on wifi.
- How frequently you usually open the app: if you open an app only once a day or every few days, it won't get refreshed very often.
- When you typically open the app: if you usually open NYT Now around 7am, iOS will allow it to refresh around 6:45am or so.
So any combination of these could be affecting your NYT Now being up to date in the morning. Are you connected to wifi and plugged in overnight?