It sounds like that IPP and the move bat files are running concurrently that the bat starts some time after IPP starts and that it copies the files from the processing folder to the archive folder then delete the files in the processing folder before IPP has processed all the image files. Are you using widows scheduler to run a bat command file? I have not use a droplet to start Photoshop in years and don't understand what you mean by a three action droplet. are you creating an droplet the use a single action that plays other actions?
The Process should be done is a single action that use two scripts steps so they are done in sequence not concurrently.