I had my first flat ever on a tandem today. The comments here were well in my mind. It just went soft, no blowout. I was carrying a minipump, a 16g inflator (1), and a spare tube (1). Couldn't find the source of the problem, which was a little worrying. Filled the tube a little for assembly, then a little more after, then went to the inflator. Thought I got it all, but wasn't quite sure, there was some pressure left when I unscrewed the cartridge. Not a whole lot. About 90-100 in the tire (700x28).
This was after more than 2000 miles, so I guess it is ok. Tire is getting thin in the middle, but I will remove and inspect carefully tonight. I still wish I knew what caused it; it would give me confidence that it just won't happen right away (we rode about 8 miles home after).
The thing is, with my wife on the back, I have no one to call! That little safety net has let me just drag one (tubular) tire and inflator around for ages on my single, but I just don't feel confident getting further away from home with nothing left on the tandem. So I probably need to carry two cartridges and two tubes to have some confidence on the tandem. Maybe a good pump is a better idea and I can just deal with the tubes.