You can back up your EndNote library by making a Compressed Library.

When you incorporate your EndNote library (.enl file) and your associated data folder (.data file), you create a Compressed Library. It is a smaller file than the .enl file and .data file combined and can be easily stored on a flash drive.

• Open EndNote via Athena
• Click File > Compressed library (.enlx) ...
• Choose if you want to e-mail it to yourself, and which references you'd like to compress. Click Next
• Save your Compressed Library