Resource Delivery is set for automatic, yet everyday I have to go into
the base, click production, and refresh my browser for it to appear in my messages.
I tried setting it to claim for a week, and switching it back, but it still happens.

automatic is random. you should set it to claim shipment since some players may have it shipped at night. lets say I dump my resources and the shipment arrives two hours after I go to sleep then the rest of the hours will be lost since my artifact points are full. it also helps to have people be a bit more active

Random? How is it random when you have a timer?

Next Shipment Delivery: ##:##:##

The timer next to that message is when the next shipment is available.
If it was set or "Claim", that's when I can claim it.
But, since it's set for "Automatic", it is supposed to do it for me when the timer hits 0.

with automatic you have to actually look at the production page before it will deliver, however any legion member can do this and the shipment will be sent to everyone. it is the same as the trellith influence where your productions will not be altered until you have looked at the production page of your planet you have used the ability on, you have to click on the page for the game to register the change that has been made.

Your productions are altered, the page just needs updated.

?

Giving me planets? How kind!

As Sahil said, you've got to trigger the automatic shipment... Ironic, right? To be honest, I'd just go with manual shipment.