The reasons they didn't sack him were pretty obvious:
1. a lack of suitable replacement that would suit their style and be substantially better than Ten Hag.
2. They identified the structure/environment wasn't good enough for a manager to succeed in. Ten Hag was therefore afforded more time to see if fixing that alone would be enough, it doesn't look to be enough.
3. Gaining a reputation for being trigger happy, also the Fa cup win weirdly changed the fan sentiment massively. So, it added pressure of sacking a manager on a high, and a feeling of what would have been if the next guy wasn't immediately successful.
Regardless of the decision to extend his contract, he won't be given the same leeway he had last season if we continue on this trajectory. He will be sacked by Christmas. It's shocking that despite a full change of coaching staff, the gap in midfield and defense have persisted, probably due to Ten Hag insisting on his tactics.
We have a good squad that should be fighting for top 4, lots of exciting and potentially world class talent in the academy too. The pieces are set now, all that's needed is a world-class manager to bring it all together.