What is causing my car's engine to die randomly?

It happened once, for the time, yesterday. I was driving along in my 1989 Ford Laser 1.3L Carb at 70kmph when all of a sudden, the engine stopped - without warning. Brakes worked fine but lost power steering. Car still had power as I was able to use my indicators and the clock was still working. So I pulled over to the side of the road, turned the key, it fired right back up, so I continued my journey.

It happened again this morning while travelling at 80kmph. This time I tried to start it while still rolling but to no avail. So I pulled over and it took about 10 seconds to start back up. It happened again today while travelling at 50kmph, but this time there was a little cough and splutter before it died completely. It happened a few more times today, even after putting in four new spark plugs. It seems to be getting more frequent though.

Anyone have any idea as to what the problem could be?

Usually this is a symptom of a dying fuel pump.

Tough one, the problem has to be constant so a mechanic can recognize and fix the problem
If i was a betting man i would put my money on the electrical system, the problem seems to be temperature related
i think it will eventually let you down
i would take a chance and take it to a mechanic, see what he can find
its a bit of money throwing and brain ( oms and volts readings ) work

I had a very similar issue with my ranger… Turns out the fuel pump relay was over heating and cutting off after it got to hot but would work once it cooled off… I would try it and see if it helps only 10$

Fuel pump issues (sometimes vacuum in tank so open the cap), blocked fuel filter. Faulty condenser /coil? Ask your local garage to check these first.