I don't know when it was released, but now googling for ' "always on" USB battery ' led me to the Voltaic Systems V15 and V44 -
What is Always On Mode?
Always On means that the output of the battery or power bank does not shut off after a set amount of time. It stays on.When shipped, most of our batteries are in Auto Off Mode.
[...]However, there are times when you want to prevent the battery or power bank from shutting off when there is little to no power draw. With an Always On battery, you could power GPS tracking devices, perform time-lapse photography with GoPro and other cameras, or run Arduinos and Raspberry Pis. Essentially, if you want to power a device over several days, weeks, or months without human intervention, then the Always-On Mode is a good fit.
As of posting, the V15 is 35 dollars on Amazon
I haven't tried it out, but it sounds promising....
I also see that several Amazon reviewers of various RAVPower power bank chargers have mentioned using those for Arduino and/or RPi.