I am not sure why you are having these issues, howver many users have reported issues saving or exporting in recent times. What version of Photoshop and what OS are you using?
Your workflow of placing an image into a template, deleting the image and repeating will unfortunately build up a lot of photoshop:DocumentAncestors metadata over time, as each time you use the place command a record of the placed document is added as metadata to the template file. This may or may not be a problem for you, however, it is good to know what is going on:
Thank you for the insight! I've changed my workflow to discontinue using that template set up. I am still having saving/exporting issues. Very frustraiting to create something than not be able to save it properly. Any other insight would be super helpful!