Cannot save "functions.php", forbidden and 404 errors

I’ve been having this problem for about a week now without tracking down a solution. For no apparent reason (nothing changed prior to encountering this error that I can think of), I cannot save the functions.php through the WordPress control panel. Attempts to save result in this message:

Forbidden

You don’t have permission to access /wp-admin/theme-editor.php on this server.

Additionally, a 404 Not Found error was encountered while trying to use an ErrorDocument to handle the request.

I have determined that this is theme-specific. If I activate a different theme, I can save that theme’s functions.php file. I can also change all other theme files in the theme I am using, so the problem is solely with functions.php.

I was playing with permalink settings prior to this error, and if I change the permalink structure I actually get a 403 error instead of the error above. That’s odd, but I can’t for the life of me figure out why they’re related. I put it back to the WordPress default and I get the error message above.

It doesn’t say anything about “read only” permissions in the dashboard, and I don’t know how that could have changed. It was working one day, then a few days later, nothing.

Anyone know what’s up? Is it a WordPress problem or a server problem?