I has exactly this same problem with a 1V I bought on Ebay from Japan last year. I search the web and took it to camera shops and the consensus was it need a shutter replacement. I returned the camera to seller for full refund and bought another from him. It has been absolutely perfect.
I don't think the comments here are truly representative of the 1V's performance. Everything mechanical needs maintenance. I think it is one of the finest cameras I have ever used.
I also suspect that mechanical objects with delicate mechanism that are stored unused for long periods fare less well than those with regular use. That could be a factor. It's not unusual to read of someone finding slow shutter speeds hanging on an old folder, for example, and then comment that after firing the shutter a couple dozen times it seemed to start working.
I'm having this issue, too, and only at high shutter speeds like the OP (which I don't think he ever suspected, it's not random.) Does anyone know what the fix is (if someone wants to DIY it)?