I just tried this on my test server and I had no problem saving a Solr configuration with 777 permissions… but a few thoughts:
1.) Is it an SELinux issue? You need to set modes in order to allow Apache to write files when SELinux is enabled.
2.) Is it an ownership issue? Does changing the file ownership to apache help?
3.) Is it a locking issue? Does it make a difference if Solr is running or not running?