Whenever our battery runs to zero, or if we have a reset due to voltage droop, the unit will not auto-connect and the user is forced to "forget" the device in iOS bluetooth settings and then re-pair with it.
The device is running SDK6.1 SD7.1. It's a nRF51822.
Perhaps this is because the pair-bond keys are lost during reset? Can the necessary information be stored in non-volatile memory?
Sure, there is no automatic NVM storage mechanism so unless you implement it yourself then all data are lost during reset or power off/on event. And yes, you can be storing pairing information in the flash. There is even example in Nordic SDK which allows you to store several peers (if you want to stay on nRF51 SDK v6.1 then see device_manager_xxx in .\nrf51x22\Source\ble\device_manager\).