Ugh. That’s frustrating 
A little background: That warning notification is a “dead man’s switch”. Meaning that Arc isn’t sending the notification itself, because by the time you get the notification Arc is already dead and dead men can’t speak. It’s instead scheduled ahead of time, while Arc is still alive, so that if Arc is killed then the notification will arrive to tell you. Much like that thing in movies where someone says “If I don’t call my partner in two hours they’ll know I’m dead, and they’ll kill the hostage / burn the money / do some other silly thing”.
Though that doesn’t explain why you got the notification so late. Arc schedules the notification to arrive either 1 hour in the future, or some calculated period of time in the future based on when Arc thinks you’re likely to leave the place you’re currently at. So let’s say you’re at home and Arc thinks you’re likely to leave home at 8am. It will schedule the “dead man’s switch” notification to arrive at 7:50am, so that it arrives before you leave.
The point of doing that is so that if Arc gets killed while you’re at home (for example), but then gets restarted automatically again before you leave, there wouldn’t have been any gap in the timeline, the notification wouldn’t have been necessary, and would’ve instead just been an annoyance.
So I think one of two things might’ve happened:
- The notification did arrive at the scheduled / opportune time, but it got missed in the clutter of other notifications at the time, as often happens with notifications we wish we’d noticed earlier.
- The notification arrived very delayed, due to iOS not honouring Arc’s request for the delivery time. This unfortunately happens far too often - iOS treats all requests by apps as just that: requests, not commands. And then heartlessly chooses to either honour the request, ignore it completely, or follow up on it much later.
Aside: The same is even more true for “push” notifications. These warnings from Arc are what are called “local” notifications, meaning that they’re requested by the app directly on the phone. While a “push” notification is a notification sent by a remote server to your phone. The notifications you see on your phone each day come from a mix of local and push, but likely the majority are push. (Aside: There’s no way to tell whether a notification was local or push - they all appear the same).
iOS is notorious for coldly ignoring push notifications until it feels in the mood, much to the frustration of developers, who are screaming, “But the customer really needs to get this notification when I send it! Not six hours later!” But screaming won’t help - iOS is king, and treats all requests like a moody child king in Game of Thrones, honouring one, ignoring another, then sometimes even killing the messenger when the mood takes him.
Sounds like probably Arc and Arc Mini both got killed at the same time then. That’s frustrating. They’re supposed to be there to back each other up - if one gets taken down, the other can take over. But if both get killed… 
iOS sometimes does mass purges of running apps like that when something has gone wrong or conditions are extreme. On older phones it can happen just by opening the Camera app, due to the Camera app needing almost all of the phone’s memory for taking photos or recording video. iOS will then kick out almost every app from memory, to make room for whatever the Camera app wants to do.
On newer phones (let’s say iPhone 11 and newer) there’s less risk of that happening with the Camera app, because the newer phones have much more memory. So if iOS does a mass purge of apps on a newer iPhone it’s more likely to be because something went weird with iOS or the phone itself, and iOS decided to deal with the weirdness by following basic tech support advice and “turn it off and on again”. You might have seen this happen on some rare occasion - everything freezes / gets very slow, then suddenly the phone resets to the Lock Screen as though it’s just been turned on. All of the running apps will have been killed, and iOS also (sort of) turned itself off and on again, to start fresh. A weird thing, and definitely not helpful for apps like Arc and Arc Mini.