I understand that this comes a bit late, but that's due to most users on this site being volunteers. Sometimes, something slips through the cracks.
How are you adding the headers? And how are you trying to edit the headers? If you are using the header/footer feature, then you cannot edit the header text directly, you should use the header/footer function again and modify the existing header. The problem with the header overlapping is very likely caused by a variation in your page layout throughout the document. If that's the case, I would add headers only on sections that have the same layout, and then change the location of the header for those pages with more text or text closer to the top edge.
I would still like to understand why your page text is being deleted, so if you could provide a step by step process, I would take a look on my Mac to see exactly what's happening. If you can provide a sample file, that would speed things up even more.
Thanks for the reply, Karl. I'm an author. I write in Word, then transfer to PDF to finalize and send to publisher. (Must) In previous version of PDF, I would use the header tool to input headers. Different on different pages. Then I edited the headers. No problems. Now, two problems. When I put in headers either with PDF tool or from Word, the regular text box on the page rises up and covers the header text on many, not all, pages. As in 3, 28, 54, 116, etc. This means I cannot just click on the header text on certain pages and delete it, which is what I want to do. I have now figured out how to do it, but why the change from previous version? Why does the text box on the page rise and cover the header boxes?
I've tried with a number of different documents and different headers, but I cannot reproduce the problem you are describing. If you have evidence for Acrobat DC working differently than previous versions, you may want to report a bug: Feature Request/Bug Report Form