I had a similar problem years ago with a Peugeot 305.
Sounds like a blocked breather pipe to the fuel tank. Creates a vacuum that builds up until no more fuel gets through.
You stop for a while, the vacuum disappears as air seeps through, then you go through the same performance again.
If you take the fuel cap off and there is a hiss, that should confirm it.
If so, find the blocked breather pipe and clear it.
The breather pipe on my old 305 had got blocked with mud at the end. A bit of poking with some strong wire cleared it. The car ran fine after that.
ChicksFan, October 2011
