Turns out my problem was the 12V power supply I am using.
When I run on batteries it works fine.
Although the PS came with several different size plugs I think maybe none of the are the correct size.
I will do further research.

I bought another power supply (12V 5A) with 5.5 / 2.1 mm plug.\
Same problem. Anyone got a power supply that doesn't drop WIFI/Ethernet connection when turning on camera?

Have you tested your power supplies with a VOM? Do you use a USB hub?

I have purchased inexpensive power supplies in the past that were incorreclty labled. I've heard that some inexpensive wall warts also don't give very clean DC power. (I.e. spikes and brownouts.) I would think that if the plug size is incorrect, then you would get no power at all since a proper contact would not be made. Furthermore, I find that my wifi dongle drops easily when it is connected to my RAPIRO using a USB hub and the batteries are even just a little bit low. (I have only used eneloop batteries with my RAPIRO so far.)

My understanding is that the Ethernet port on the Model B Raspberry Pi is very power hungry. So if there's a dip in the power source, I can understand that this would be one of the first functions to stop working too.

One last thing: I found that the digitalWrite(POWER, HIGH) call that enables the servos all at once draws a lot of power very quickly and will create a brownout on the Raspberry Pi, which will reset my wifi dongle sometimes. This is especially true if it is connected using a USB hub. This happens in the setup of the provided sketch. I added a #V0 and #V1 serial command to power the servos off and on. Sometimes after a power on I need to wait 30 seconds for my wifi dongle to recycle before I can ssh back into the Raspberry Pi.

I have not been able to keep stable connections with the wifi and ethernet connected simultaneously so I think you are right about the ethernet port. Also with the LEDs connected I drop connection sometimes at power on so that makes sense to. I not sure I understand what you mean by a #v0 and #V1 serial command to power the servos off and on.

I hope the Rapiro folks will modify their DC to DC converter so that it supplies enough clean power to prevent disconnects. It is very frustrating. I gave up trying to use the camera because I just couldn't stay connected.