Guerrilla Mail keeps all incoming emails for only an hour, so if you can't check in on your inbox for a while - the emails will be lost. A way around would be, of course, to periodically fetch and store emails locally.
There's a python client that automates low level operations for GM (list emails, get an email), so it's easy to add another command to it to combine list and get commands together, to get all emails and save them into files.
Here is a patch that adds the command, using it is easy:
$ mkdir inbox
$ while true; do python guerrillamail.py getall inbox && sleep 60; done