I’m having the same issue, I believe. I’ve added custom fields to a home page using the default front-page.php as a template. I can add data to the fields, but the data won’t save.
I set the page to a named page template, and the problem was solved.
Update: I removed the named page template, removed the front-page template and reset to default. I could save new data and display with the now default page.php. But here’s where it gets weird… for the heck of it, I put the front-page template back in the direct, re-entered and saved new data… and it worked.
