Correct permissions for Writable folder?

If your dir permissions are correctly set, worth taking a look at this as it could be to do with permissions of the httpd in SELinux.

This worked for me (Centos7):

A simple check to validate:
1) Create test.php in app root
<?php file_put_contents("/var/www/html/<codeigniterpath>/writable/test.txt", "test");

2) Execute it from command line. It should create the file with test inside.
Then delete test.txt.

3) Call from browser https://url/test.php

If it doesn't create, check /var/log/audit.log, look for "denied { write } " relating to the httpd/apache.
If you find these entries, then it might be to do with permissions for httpd in SELinux.

Try:
chcon -Rv --type=httpd_sys_rw_content_t /var/www/html/<codeigniterpath>/writable/

or google "SELinux apache write permissions" for clues