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If these are normally stored on your P: drive, then, when you are disconnected from the network, they will be unavailable. One option is to store your libraries on your laptop in any folder - so long as you can find it e.g. C:\endnote. Another is to keep them on a memory stick. Whether you retain copies on your P: drive is up-to-you but it is strongly recommended that you do keep copies because libraries on your laptop or memory stick will not be backed-up at all. Making Regularly saving a regular copy back to your P: drive will provide security.
Note that if you are copying Endnote libraries, that each library also has an associated data file which must also be copied. So for example, in this directory listing there are three libraries - highlighted in the same colour are the corresponding data folders:
Depending on your computer settings, you may not see the suffixes (i.e. .enl and .data).