Exact same symptoms we experienced on our Hyundai Getz. Actually happened twice on same car. First time fixed under warranty, then by myself.
Called the RAC out first time it happened and his diagnostics test was a bit vague and between us we guessed it might be the crank sensor. We thought the car was out of warranty due to doing my own servicing. However, when I telephoned my dealer to order the part I was advised my car would be repaired under warranty. What fun we had taking the car into Glasgow, about 40 mile trip. Car would stop every few miles, pull into hard shoulder and wait for it to start again. Disconnecting the battery for a few minutes always seemed to help.
Anyway, avoiding a long story it was the crank sensor, and it went again about a year later and I fixed it myself. The original replacement had been poorly fitted and was destroyed in situ by moving engine components.
Just read the OP again, and driving slowly did increase the chance of stalling. Keeping the revs high did put off the inevitable stall for a wee while longer.