I had been using the default page templates on a development installation of WordPress which is a direct copy of another WordPress installation. During the process of editing some pages I decided I wanted to try a couple different types of page templates. The templates were exact copies of the default page view but with one line of code modified such as not displaying the title of a page.
After creating numerous page templates I went to apply one of the templates to an already created page and to my surprise none of the templates showed up. The page template field didn’t even show as an option in the page edit screen as shown in the below image.
I then attempted to add a new page to see if the template attribute would display there however it was not showing there either. I checked back on the live copy of this exact WordPress installation and page templates displayed there without issue. So I knew that the configurations were a mirror copy minus the domain or any direct path variables. The issue had to be in some sort of session or in something stored in the database.
Resolve Missing Page Template Attribute:
After attempting various solutions and verifying that all of the files were similar to the live installation of WordPress where the page templates were showing as a configurable attribute I finally figured it out. For some reason setting the theme to the default theme and then back to the third party theme I was using resolved the issue. To change the theme you are using click on Appearance in the left navigation, click the Themes sub option, click the theme you are going to temporarily switch to, and then click the Activate Theme Name link located in the top right corner of the pop up display of the theme. Once you have switched to the new theme simply click back on the theme you are using as your default theme and click the Activate Theme link located in the top right corner again.
Verify The Theme Is Correct & Verify Page Templates Are Available:
Once you are back on the theme you were initially using load your site to make sure things are displaying properly. Once verified go back into the WordPress Admin and see if the Page Template Attribute is available as displayed in the below image.
Now you can test out new templates on each of your pages. I have never seen the page template attribute not show up before and I hope to not see it again though I know in the future there is an easy fix if it happens again.