It sort of sounds like a bad connection in the wiring harness somewhere. I presume they checked the battery and alternator at the same time they cleaned the battery terminals. If not, that’s something to try. Another simple thing is to remove everything from you key ring, and only insert the single key into the ignition, see if that helps.
hmm … when it dies like this, there’s no “rrr rrrr rrr” sound or even a click when you turn the key to “start”? Do you have a security system that prevents car theft by disabling the starting system ? If so, that could be the cause.
Were there any repairs, even an oil change, done just prior to this starting? Any big rainstorms where water could have splashed into the engine compartment?