Comment by mtndew4brkfst

If lack of a successful ACK means you retry indefinitely until you do get an ACK, then whichever side handles deduplication need to store all observed messages indefinitely or you may deliver the same message more than once without correctly deduplicating it.

If instead you only store them for N days but an ongoing retry loop finally succeeds in N+1 days, you get duplicated delivery.

If a retry loop gives up after finite elapsed time, which sets a ceiling on how long you must retain observations, then you do not in fact achieve at-least-once delivery without using a lesser qualifying statement.

One of those constraints must be compromised on. That doesn't mean a practically useful implementation can't exist, it just means a theoretically ideal one can't without the infinite memory.

Many systems and real world processes would actually suffer negative consequences if a weeks-old payload was delivered-as-new, so hardly anyone balks at this part of the implications. But again, you have to redefine at least one of the claims (or acquire infinite memory) to have a coherent system that fulfills those claims.