The feature you want is called **pass-through charging** by some. It's not typically incorporated in "power banks" because [it's not good for the battery](http://community.anker.com/t/which-portable-chargers-support-pass-through-charging/31361). 

You may wish to consider a commercial UPS [(examples)](https://www.walmart.com/browse/ups-battery-backups/c2hlbGZfaWQ6NDU2MDczOQieie) for this function. The battery is either charging (normal), or discharging if the AC power is disconnected.

Another commercial product that may accomplish this is a *dual redundant power supply* ([example])(https://www.jameco.com/Jameco/Products/ProdDS/2304391.pdf). 

Still another way is to use a "wired-OR" power arrangement to supply power to your RPi. There were some answers posted recently that described how that works: [Answer 1](https://raspberrypi.stackexchange.com/a/115894/83790), [Answer 2](https://raspberrypi.stackexchange.com/a/111599/83790)