Yay a fax question!
Ok so what you described here seems very common. Old fax machines work better than new fax machines, such is the nature of the beast. There is no development being done or money to be made in traditional faxing. New fax enviornments are also entirely digital where they used to be all analog. This has some profound issues with new fax machines that come with features to handle digital but often do a poor job of it.
Heres what you do:
1. Perform a Cold/NVRAM reset on the printer to wipe all fax memory and settings
2. Reconfigure the fax machine however you like
--I normally like to configure it as simple as possible while troubleshooting
--i.e. Fax modem > 2 wire fax line > fax machine
--Add in splitters, handsets and whatnot after you got it working at a basic level
3. Disable ECM (Error Correction Mode)
4. If customer is on DSL then suggest looking into a DSL filter
Pending if your customer is truely a high traffic faxer or not what is most likely happening is that bad fax messages are getting stuck in its memory because the fax machine doesnt know how to hang up. It never recieves that hang up tone and times out its connection, chewing up your memory as it goes. Disabling ECM seems to always be the solution to clean up those calls so they can be properly answered.
If your customer is really a high volume fax person then suggest a more dependable service such as Online Fax. Personal fax machines cannot compete with these new email based services in terms of performance and reliability. Run those legacy fax machines into the dirt, then swap them with a nice scan to email MFP and cancle that hard fax line to the home.
More info regarding online fax: