What reason would a 1988 Camry cut off while driving and not crank back up?

There could be many reasons including fuel filter igition components ect. If you go deeper than fuel filter then it would probably be cheaper to invest in a 1/2 hour of diagnostics from a trusted local garage. Dealer prices are usually out of reach. Good luck

We have a 1987 Toyota SV21 Ultima that had a similar problem. We could drive for about 20 minutes normally and then the car would cut out and not restart. If we left it for half an hour or so it would start and drive normally to get us home. The fault was in the igniter box. Over the years the wires inside had fractured but remained in contact when cold. As it heated up during use expansion caused the broken ends to separate, breaking the ignition circuit. Soldering the wires together fixed the problem and it still runs very well after many years service. Hope this helps.