Honda Civic Forum : “why would the car start and run fine, but after 20 minutes or so die, and not wa...”

What you've explained could be hundreds of things.  We need more in formation.  Was it acting funny before(was there any noticable changes in either gas milage, any funny smells, leaks, or any drivability changes, overheating?).  Also did the car start back up after a while of sitting? what happens when you try to start it up?  Is it cranking at all?  If its not cranking at all is probably something electrical.  If its cranking and not turning over check to see if your fuel pump is priming and that your intake tube, and fuel system is all connected and not leaking anything.  either way before id do anything id check all the fuses and relays

more details please...

main relay

Igniter switch in your ignition. This typically happens when the car has been running for a while, then heats up and cuts off. Honda's have been known to do that.

I agree with David and James; could be anything and you've simply not provided enough information to trouble shoot the issue. Disregard the annonymus comments...they are guessing and will have you buying parts you may not need.