Quite often it doesn't. This morning I was waiting for neighbors to respond to my request for conjured candy and did some battling, mining, completing bingo cards, visiting neighbors but it wasn't until I closed and reopened the game that my response went from 0 answered to all 5.
Also, when I was having trouble opening the game the other day, I got the canned response from Storm8 that they are not responsible for lack of cell reception issues, despite the fact that I told them Bakery Story is still opening so obviously it isn't connectivity issues. It is VERY frustrating that Storm8 seems to have no customer service s****s or willingness.