That's a new one. If it explicitly shuts down *all* traffic through this device, then it should be pretty easy for the device manufacturer to reproduce.

21 hours at 15 second intervals is 5040 samples. Maybe it's just that number of ICMP Echo packets (period) that's causing the problem. Try cranking your packet rate down to 1 second (or, depending on your network capacity, even lower - like .25 seconds - you can manually enter that) and see if it reproduces at the same sample count. If it does, then try switching to final destination only and see if it still happens (or maybe takes longer). It might take longer (like, say, 4 times longer). If so, then see how many hops you have past the failure point - and see if that corresponds to how much longer it takes to fail with final destination only.

It could also be a problem with returning ICMP TTL expired packets (or echo replies).

It sounds like a bug in the hardware, though, and you should probably talk to your UTM box manufacturer about it. The "suggestions" above just relate to narrowing it down a bit so you can better report the problem to the manufacturer.