1984 Laser: Dying at Normal Speeds

My 1984 Chrysler Laser Turbo died three times on a trip.
The first time I was driving along at 60mph. I was able to
re-start as it coasted to a halt. The second time I was also
driving about 60 mph. It died. I cranked it almost until
the battery was down. Then I coasted it down a hill; it
started at the bottom of the hill. I thought it might be
a clogged fuel filter so replaced it. It died a third time
this time driving about 30 mph in a city. Again I had
difficulty re-starting after it had stopped.
What are the possible causes?
Thank you.

--
Jonathan Grobe Books
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