Chain hit blessings are powerful on paper but in practice they suffer from too many limitations. If you miss the target, or block, or push, the combo resets to zero and you have to start again.
While the former two make sense, I don’t think pushing should break an attack combo if you immediately chain into the push-attack right afterwards. On some weapons the push attack is better for certain things like single target damage or horde clear and it is common to incorporate them into combos.
You don’t drop chained hit stacks when push-attacking or being interrupted anymore. It was an unlisted(ish) changed in Patch 13. You now only drop stacks when you miss an attack.
It’s intended design. Skill vs reward. Chained Hits Blessings are meant to reward you for controlling your melee attacks, instead of just spamming hoping they connect.