How did Binchou-tan's grandmother die?
This is explained in the last (4th) volume of the manga:

 She collapsed and passed away at a market when she went to a town.


The respective page:


Image taken from livedoor, a Japanese blog

Translation:

 2nd - 4th panel: Good afternoon. You're Binchou-tan, right? I'm a spokesperson from town hall... your grandmother passed away in the town. Yesterday at the market, she collapsed, and...