You bulbs seems reset to factory default after the power outage, otherwise you won't see any wifi signal coming from the bulbs.
So the bulbs won't associate with the access point automatically, because they are not just simply offline.
If the bulbs just go offline, normally a restart will help to make the bulbs reconnect to the access point.

I think it is normal to go through the setup process for each device, the phone can only connect one bulb's wifi each time.

Agreed. I wonder what event triggers factory reset? It seems to be a bit of a tricky issue with light bulbs I have a couple switched outlets and they don't have this issue but they have a button to press to force reset.

I understand that the app can only deal with one device at a time. It gives me the SSIDs of all known devices but without linking that to the information it knows about the devices such as the name I have given it. I can then select a device to configure but the app fails to complete the operation.

(I did see a mention in another post for how to update firmware and have done that so both bulbs are now on 1.4.3.)

Thanks!

I see what happened. On the Amazon page for one of the bulbs I see the warning
[COLOR=#888888 !important]Beware of turning the power on and off 3 times quickly as this will reset the device
This is not a good solution to the reset problem. Standard operating procedure for a power distribution system breaker when it interrupts a fault is to close back into the fault at varying time intervals to attempt to restore power. Normal operation is to reclose three times. Typically this will start with a shorter interval such as 1/4 second with subsequent intervals being longer. The intervals and reclose count allowed before the breaker remains open are configurable so this will vary depending on local conditions, utility philosophy and need to coordinate with upstream protective devices.

This explains why both of my light bulbs reset to factory defaults following the outage. When our power goes out we can see the recloser operation as power comes on momentarily several times.

I suggest that the engineers developing the firmware for the bulbs consult with a utility systems engineer familiar with protection and develop a strategy for factory reset that does not unintentionally coordinate with typical power distribution system operation. I would suggest simply increasing the count to 10 would resolve this problem as it is nearly unimaginable that a utility would configure their equipment to reclose that many times. Closing into a fault causes measurable damage to power systems equipment and is only done to attempt to restore power. (For example a lightning strike that flashes over a lightning arrestor will be interrupted on the first trip and the reclose will be successful. A small branch across a wire may burn off and on the second or third reclose and result in resumption of service. A wire down and literally shorted to ground will not clear and continued reclosing will only result in damage to transformers and other substation equipment.)

For more information see https://en.wikipedia.org/wiki/Recloser or search for "typical recloser timing" and you will find a lot more detail.

I hope this is addressed in a firmware update for the bulb or I am doomed to have to reconfigure the bulbs following any power outage that results in recloser operation. I'm sure I will not be alone.