routers get reset ...

I have been having problems with my ISP/the actual network owners (Verizon). Basically, my connection to the Internet starts slowing down to the point that my data connection and VoIP telephone (same company (same mistake!)) stop working
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I troubleshoot the problems from my side, but they keep giving me sh!t telling things like "routers get reset".
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Do you know of best practices, when it comes to monitoring your own connection to the Internet to prove that "routers DO NOT get reset ON THEIR OWN" just like that, that there must be something going on? I could run tcpdump to monitor my network, but I think you must match your logs to theirs to prove/legitimize your point
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What legal issues are at stake here? Can you legally force your ISP/Verizon to give you access to the logs of your own connection to the Internet?
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lbrtchx