I'm getting a p0745 trouble code on my 03 explorer XLS 4x4, keeps coming out of gear

Hello, this code relates to an electrical concern with the internal electronic pressure control (EPC) solenoid function. This does not mean the solenoid needs to be replaced, but does indicate there's some kind of concern that will require testing, possibly internal. A wiring harness inside the transmission could be a concern, the solenoid or more than one may be a concern. You've done all you can by changing the fluid and filter -- which is pretty exceptional on this 5R55 transmission, as it's not easy to do - nor is it easy to refill with the proper fluid to the proper level without correct tools. A diagnostic tool that is capable of monitoring transmission operation is needed as a first step of understanding what is happening with the different components when the problem occurs.Then a wiring diagram and workshop manual is needed to pursue further testing. Keep in mind - it's an aged vehicle with probably higher miles (unsure about the miles from your question, but just relative to the vehicle's age), and often times it could be something impractical to repair or requiring tear down. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops