MacBook & iPhone require Apple ID all the time.

I have a Macbook air (2015, OS 10.13.2) an iPhone (6 Plus, iOS 11.2), and a 2015 iMac. All software up to date.

I am asked to log in with my apple id every time I use an app that may request it - Both on my phone and computer.

All three devices are trusted, authorized, verified. I use LastPass, and AppleID is set to Auto Login.

I've checked preferences for system, iCloud, iTunes, App Store, and anywhere else I could think of that might be able to turn login back on.

The only places I checked "Always require Apple ID" are iTunes & App Store - for purchases only. Free items do not require a login.

I've shut down and re-started. Still am asked to log into Apple ID over and over again - and sometimes asked if device is Trusted.

Possible culprits:

-- iPhone: stopped working last week Apple store "genius" said that model was faulty and nothing could fix it. Apple wasn't replacing them - just a discount to buy a new one. So I did & restored from the Cloud backup

-- iMac: yesterday I brought it in to the "bar" - it's been messing up since I bought it, so it's back in the shop.

-- Airport Extreme; yesterday too - it started making clacking noises then screeching. It was replaced.

How do I get my devices to keep me logged in?