WordPress 3.7.1 update fails; cannot copy files

Hi,
I’ve been all over the web on this so hope you can help. I’ve got several wordpress sites and have had no trouble updating them except for one, and I cannot figure out why. I get an ‘installation fails, cannot copy files.” I have given permissions all over the place but just can’t figure it out. My domain is hosted all under one large accout at my public ISP (apache) and then I have several sub-domains, this one being one of them. Point is, they are all on the same server.

The manual instructions look daunting and confusing and I would really like to figure this out. I can add new plugins, just can’t get this one thing to work. Any advice would be extremely helpful.

Thanks!
Debbie

site: reelingsilk.com/academy