Ok I did that too.

Yes the problem comes from file writing permissions.

In your site wpforo have not a permission to write into file 

/wp-content/plugins/wpforo/wpf-themes/classic/colors.css

The right way to solve this problem is fix files and folders permission.

All files in FTP to be have a chmod 0644 and folders to have chmod 0755

The another way to fix this problem.

1. Open file /wp-content/plugins/wpforo/wpf-includes/wpf-hooks.php
2. Go to line 1025 and change this code line  to this code 

wp_add_inline_style( 'wpforo-dynamic-style', $css );

3. And Go to line 1028 and change this code line to this code 

add_action( 'wp_enqueue_scripts', 'wpforo_dynamic_style', 12 );

after all changes save this file into FTP and try refresh Forum Page with Ctrl + F5

Ok, thank you very much!