The reason you see this error in the first place is that your computer doesn't have enough storage for Aftershoot to save its AI cache files.
There are 2 ways to fix this issue:
1) Freeing up storage on your internal disk
To do this, the most common places to look are your Trash or Recycle Bin, Documents folder, Downloads folder, and large apps.
Delete any unused files or apps and also remove them from Trash.
2) Changing the path where Aftershoot's cache files are stored
The second option is for you to instruct Aftershoot to save its cache files at a different location than your home disk.
This could be a different drive than your default C drive if you're on Windows or it could be an external drive if you're on Mac.
To do this, you open Aftershoot and go into Aftershoot's Settings/Preferences by clicking on the top right.
From there, go into the Import/Export section and change the entry that says "Path to Aftershoot's cache files"
Change that to the disk you want to use and restart Aftershoot. You should be all set!
Note: After changing this entry, you won't be able to access your older albums so make sure that you've finished working on your older albums before you change the cache path.