1984 VW GTI dying when not accelerating?

Hey there,
My 84 Rabbit GTI is having an interesting problem. When the car seems to
have warmed up, the engine cuts off when I take my foot off the gas. For
example, braking and coming up to a stop sign, or slowing down to make a
sharper turn; when I am not accelerating, the car will die. No shakes or
noises, all electrics stay on, just no power to the engine. If I can catch it,
revving the engine will save it. Once it dies, I need to have my foot on the gas
when I start it or else it will crank longer than it should. Any ideas as to how I
can get this fixed would be great! My first order of business is to change out
my fuel filter, but I am waiting on that to show up in the mail.