For several months now, I've been using an app called Due for reminders, and I think it is helping me more than any other app I've tried. It has interactive notifications that let you reschedule or complete reminders from the lock screen; Siri support; a set of really nice sounds that can be chosen per-reminder; all the usual recurring features; and best of all, customizable auto-snoowhze, which causes the reminder to repeat until you either reschedule or complete it. Its tagline is "never forget anything again", and I'm not sure the developer could have done a better job making that happen. https://apps.apple.com/ca/app/due-reminders-timers/id390017969
@menelion iOS seems eventually throttle its notifications if it's repeating the same thing over and over, but if you set the snooze time to 10-15 minutes it should still nag you for several hours before being rate limited. And as soon as you open it or another reminder comes through it'll start nagging you about the overdue reminders.
@simon Wow, thank you! am I right that it will nag you until you turn it off? That's the feature I've been searching for in all reminder apps. Like, not beep twice and go away, but reeeeally annoy me till I shut the reminder up.