It hides when other windows open, but it doesn't always come back after they've been closed.
When the game is first opened after being quit from the tray, opening and then closing one of the windows along the bottom causes no problems; the chevron hides and then reappears. However, tapping on a sub, outpost or specialist disappears the chevron semi-permanently. I've been able to get it to reappear by entering another active game from the menu. When that doesn't work, I have to force quit and restart the app.