Yes, the kukuni has limits and likely limited resources. And it is likely unable to act against its own nature. From what we've been able to glean, it only resets the loop when the perfection of the day is marred, and in Liyu's case that perfection is marred when she comes home to find her dead father. Coming back to find her home burned down, and presumably her father killed in the fire, is another instance of the day's perfection being marred. That will almost certainly trigger a reset, and even if that is costly, Zhi dies. Zhi cannot survive another reset.
The theory we're working with is that the kukuni can't actively make the day worse, as that goes against its nature and purpose, but it also doesn't have to act. It could ensure Liren lives through the day, but it doesn't. By ensuring Liyu's Perfect Day is ruined at the very end through inaction, it can reset things and do the day over and over again, repeating its moment and letting it grow more powerful with every loop. So our goal isn't to get it to expend resources, as a battle of attrition doesn't favor us. Rather, it's to close the loop. By removing Liren's body from the house, we ensure Liyu doesn't discover her father is dead. By cleaning up, we make the house nicer. By bringing a nice doggo in, we ensure she has something friendly to play with at the end of the day. With home being comfortable, there's nothing to stop the day from ending badly. The Perfect Day comes to an end on a good note, meaning the kukuni won't be able to act, so won't be able to cause a reset as doing so would go against its nature and purpose.