2004 Kia Optima keeps going dead

If this happened with a new battery then I would suspect the alternator. Lots of test that can be made on both battery, alternator and wiring. YouTube...chrisfix has a good video you need to watch. He covers all of this.

I had this exact same issue and it was caused by the crankshaft sensor would not start until it cooled down for a short time. I would crank it over and over and nothing till it cooled then it would start up again sometimes needing jumped i replaced the sensor and works fine. Warning though the first time i bought a cheap autozone sensor and it reoccured twice so i bought a slightly better sensor at advanced auto and its ran for 3 years now without issue. Also has the sensor checked first and autozone said it wasnt bad but it definitely was just didnt test bad unless i heated it first so it was hard to prove but they did refund me and i went to advanced and got a wells brand. Its a fairly simple change to on mine the sensor was on top in the front of the engine and its only one small bolt and a wire connector took me like ten minutes to fix. Hope this helps you solve your issue as well ive read since that its a very common issue but doesnt throw a code most of the time good luck :-)

could be alternator or a parasitic draw. for 100% confidence when starting disconnecting your battery terminals and the reconnecting them is a good way to make sure parasitic draw isnt the issues, after and before driving.