Not sure how to do it with the OmniPro but if you have a computer running 24/7, there are a load of (even free) software tools for both the Unix and Windows platforms to keep and eye on network connectivity. It should not be that hard to connect that modem to eg a z-wave or x-10 appliance module and signal that module to switch off and back on. Actually a simple script that send out a ping and greps or seds the result, then acts on said result is all that's needed for a Unix box. Powershell on the Windows platform should be able to do this as well.
Once I get a Vera, this is one of the things I am looking into implementing.