What could it be
My car has 60000 miles.
My car has an automatic transmission.
Since you mentioned that the motor will eventually start at times, we can assume that it is getting spark. This means that you may have a fuel delivery issue. This may happen due to lack of fuel pressure, a faulty fuel injector, or potentially a dirty or faulty idle air control valve. This valve reads the air intake into the engine and relays this information to the computer so that it can adjust the air/fuel ratio at low engine speeds or idle. When this is not working properly, the engine will usually fail to idle on its own as you describe. To have this resolved, I recommend having an expert from YourMechanic come to your location to diagnose your no-start issue so that this can be corrected.