I have tried to start my back up manually because the automatic back up isn't working for some reason. The last backup was June 3, 2015. I have the icloud backup on and I have plenty of space in my icloud!
In- order to Fix the Automatic iCloud Backup not Working issue on iPhone do the following steps ;
Delete your iCloud profile in iPhone
Now again reconnect the icloud profile
Now you get message sync automatically..
Well also , check this below article to troubleshoot this issue ;
Hope this helps...