Not sure if this applies or not, also believe it applies if using anything other than regular dial up lines at times (VOIP, etc).
From their site
HP LaserJet 3015, 3030, and 3380 Series Printers - Cannot Send Faxes Using an Extension Phone
There are some instances where the fax machine will power-cycle itself when attempting to send a fax by dialing the receiving fax machine using an extension phone immediately after the device is powered on.
This issue only occurs if an attempt to send a fax using an extension phone is the first task attempted after the device is power-cycled. This is caused by the device remaining onhook after a power-cycle. If a fax is sent from the device control panel, a fax is received, or the fax/send button and the Job Cancel button is pressed, then initiating a fax via an extension phone will function without a problem.
This condition may be corrected in a future firmware roll. When available, firmware can be downloaded from the Support & Drivers download pages on the HP Web site at http://welcome.hp.com/country/us/en/support.html. Click here to determine if there exists a firmware download, and if so, to download the firmware . Select "download drivers and software," type the product name, select the product model, and then select the link "Cross operating system (BIOS, Firmware, Diagnostics, etc.)" if it is available on the Specify Operating System page.
I would try for a firmware update first, then try it on a pots line if you have one and not currently on it.