Multi-circuit transients without breaker trip
Get a different electrician and/or make your power company come back.  It sounds like your losing one leg of your service. 

The reason your cooktop control sends it into remission now is that it starts by backfeeding the bad side of your service which heats up the connector that is burning.  The heat (or arc) acts as a temporary weld that makes it work again. For awhile.

The next thing to happen will be that the heat control on your cooktop just acts like a really big dimmer switch for all the circuits that go off when your issue occurs.

Yes, fire is a possibility but it will likely be contained to your meter can or breaker box (possibly a pole or underground connection).