I'm the author of ConEmu - alternative terminal for Windows. My users have created the issue ConEmu/ConEmu#629. When bash is started in ConEmu console, it totally ignores all extended keys (Arrows, Fn, etc.), so users can't access command line history with Up/Down arrows.
What is the problem with bash? Up/Down arrows properly cycle cmd.exe history, when it's started in ConEmu, but bash ignores them.
ConEmu is GUI application, so it get keyboard events via WM_KEYUP/WM_KEYDOWN and forward them to the created (usually hidden) real console using WriteConsoleInput.