FC cannot save changes to the Library

Message: " The hard disk where your library is located may be full or unavailable or permissions may have changed ."
I tried making some changes to a project I'm working on and I go this message - I have enough space in HD and do not know why I can't save changes? How do I check permissions?

Is your Library located on your system drive or on an external drive?

- Ronny

The library was initially on a external HD - then I moved it onto my system drive onto my desk top. I moved it here because the edit was running slow when I played it back so I thought if I moved it onto my computer it would run smoother for sound editing.
But I also upgraded to Yosemite and now I'm thinking it is all for this reason... I am now repairing permissions and hope this might fix it but if you should have any other advice please continue..

System drives are not optimal for Libraries and media.
1- What is the capacity of the external drive?
2- How much free space is on the external drive?

My external hard drive is a 1 TB, which is divided into 2 compartments.
1 side only has 28Gb available, the other side has 300GB available...
I thought that if I edit on my actual mac it would not have to travel along cables and it would be quicker - this has proved correct as the edit is reacting quicker to changes - but it's still sluggish.
Should I move library off desktop into computers HD? Or move the whole thing onto ExHD?