I bought a 1 owner 94 LeSabre with 70m miles, excellent condition but have major problems with the car shutting off while driving. Mechanics cannot find the problem (but I've been towed 6 times). Most times, after towing, the car will start right away. The have recommended everything from wiring harness replacement to computer "brain" to ignition problems but cannot guarantee any.
Have any suggestions?

Test/replace the Ignition Control Module and coils--many AutoZone stores can do this for free.