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I am having the same problem in my apartment. I have found that whenever I rapidly turn on and off the air compressor, after about 20 toggles, the Arduino Duemilanove will halt. My Arduino is plugged into the same outlet as the fridge and when I unplug and replug the fridge, the Arduino halts after about 2-6 toggles, so it is obviously a power issue.
When I say Arduino Duemilanove "halts", it resets and then does not even execute its setup function. I used some LEDs to verify this, then I eventually used another Arduino to monitor the first with the same results. This is what you are experiencing with the WDT not being turned on. The funny thing is that the second Arduino does not crash, only the first, so it has to do something with my code.
I believe the workaround is to turn on the WDTON fuse with an ISP programmer. That way you don't need to enable the WDT in software.
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we are currently using the arduino bootloader to upload code to the boards. How would you go about turning WDTON?
Also, adding a capacitor sounds like a great idea (effectively a backup power source to flatten the voltage), any way to add that to the Arduino without opening the guts of the wall wart?