Hi,
By default once you have entered the Apple ID and then the Password and ticked the Remember Me box then the app will login in again every time you launch it.
I have not Signed Out for so long (Probably El Capitan) that I have no idea if the Remember Me option is even there any more.
If your Mac was not holding the Password it is more likely the app was having trouble writing that info to the Keychain.

7:48 pm Sunday; September 9, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
MacBookPro 15" 2016 (High Sierra 10.13.x)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)