First thought is unstable power causing modem to cycle. Recycle quite often results in a new IP assignment between modem and provider. Surfbeam2 is supposed to operate between 85-264 volts and 47-63Hz, so it can tolerate spikes. But it can't tolerate hits; as in momentary loss of power. But it wouldn't hurt to put a voltage/frequency monitor on their inverter output. Such monitors are available in both hardware and software approaches, some of the latter are even free. That's not a fix, but it can determine if in fact the inverter is at fault.
If that proves impractical, an alternative solution may be a good quality UPS between the (suspect) inverter and the LAN. I have had very good luck with APC SmartUPS models over the years, they react in milliseconds. I currently have a 1500VA (laser printers need a lot of battery) on my home network, a 750VA on my home entertainment system, and a little 350VA on desktop configuration I made around an iPad. With accompanying software, you can set a voltage operating window.If the UPS detects voltage from the inverter that's outside that window - power dip/spike/loss - it cuts off supply and throws battery power at the LAN until it senses the supply has come back to within your window. The UPS restores the supply voltage, and puts itself back in monitor/recharge mode.
Alternatively, it could be a LAN address conflict. I witnessed that with HughesNet Gen4. Modem and router inconveniently had same default LAN address (192.168.xxx.xxx), and therefore couldn't talk to each other. Far as I know you can't change the SurfBeam2 LAN address, but most routers should offer LAN address alternatives in the user interface.
//greg//