This morning my village of 6 lost a Mouflon we had been working on because of despawning. I checked on it before going to bed at 3AM, and it was not ready for it's next beating. When I logged on this morning at 8 AM before heading into work, the Mouflon was gone. (Most of my people are East Coasters)
The inconsistency and short window of taming is something of an antifun mechanic. All your work on it over a period of days can easily be wiped out by a very short timer kicking off randomly over a very long period.
If we compare livestock to another late game resource, in this case Steel, we see the opposite. Both take days to bear fruit, but Steel is both consistent and predictable in it's function.
TL;DR, Taming either needs to occur consistently a set number of hours after the last step of progression or have a longer grace period for when animals are ready to pacified. The system as is puts it out of reach entirely for hermits without botting, and even villages of my size can run into trouble where days of progression can just disappear literally into the night.