Ok, so I just need a power source that won't go to sleep?
I've looked into powerbanks with "always on" features, but there are only a few models and they tend to be more expensive for less charge. Voltaic's V15, V50, V75 and V88 all have this feature. They can be used for long deployments of low power draw devices.
https://voltaicsystems.com/always-on-batteries/
https://voltaicsystems.com/v15/
Another forum post mentioned using LiPo batteries, which seems like a good option except that the total mAh of LiPo batteries tends to be much lower than a standard power bank, so attaching one of those wouldn't necessarily give me the deployment duration I need.
https://coolcomponents.co.uk/products/lithium-polymer-battery-2000mah