I'd be glad to help -- if you weren't the better part of a thousand miles away. The problem is, without looking at what you've got, it's hard to say what's going on. You could have a burr on your rim, at the valve stem hole. You say it's a vintage bike - is it steel rims? A pinched tube is a possibility for the second flat; but without inspecting I can't tell. Schrader valve stems are pretty sturdy; I doubt that 'normal' handling will rip one out in a day. Unless the tube is old and the rubber is failing.
JanMM's statement was true. Don't blame the type of valve; something else is going on.