192.168.1.1 is your router -- you can get an admin screen, check firmware version, etc. by pointing a browser to this address, but this is not the problem and so there's no need to do anything with this. If you log in to the router, you should be able to see the "default gateway" IP address for the next hop, which would be handy to have -- though you probably already have it from the tracert output.
I'd guess 10.0.0.1 is your radio -- you could try logging in and looking around to confirm, unless your provider supplied the radio and has changed the default info. I found this utility you could run that would help to confirm this in any event: <
http://www.ubnt.com/support/downloads/utilities>.
Is a.b.c.d in your output 10.0.0.1, or 10.b.c.d? Anything that starts with 192.168. or 10. is not exactly a real IP address, in that these are used all over the place. These addresses are private only to each of a great many different segments of the internet, around the edges. For example, 192.168.1.1 is used probably millions of places, so there's no issue with pasting numbers in these ranges here.
The tracert outputs are interesting. Do you see the 60 second delay even when you use the option to suppress DNS name translation? If not, this all makes sense. You really want to do a tracert to something like chiefdelphi.com when things are working and note the difference when things are not working. The idea is to look one hop past where things get when you experience an outage.
I'd have to investigate further, but your radio could have a sort of bridge mode. However, I think it is probably using a 10. address on the over-the-air side. It suspect that it has an address that starts with 192.168. as well. The utility above should help you find this, and hopefully you can log in via this address to get some more info.