In chapter nine, Maya actually wanted to save Tatejima by making him stay in the bar during the ninth of the month, because she remembered his death anniversary.
When you search up the client's name "amamori toru" on internet, you find omamori toru being amulets to protect against bad luck. I'm guessing it prevented Maya to save Tatejima, since she's probably something like "death". It wouldn't let things get her way.
The reason why she could have prevented his death could be something else though, it's not like things are easy to understand.