Could power cycling a modem 24 times a day for over 3 years (>30,000 times) cause the modem to lose its settings?
Sure, depending on how the firmware was written it may have worn out the EEPROM (typically good for &gt;100,000 writes). That's not normal operation and they may not have tested for it.
On the other hand, a cheaply designed reset circuit and memory protection could result in corruption and therefore revert to defaults from a single upset.