Ok Internet hiccups?

We are getting network latency just about daily and all day now.  The connection to the Internet at the modem is perpetually failing and coming back only to fail again.  Since we have the full Internet/Cable/Phone package here are the symptoms:

1. Playback of voicemail or recorded messages on the phone appear as if an old vinyl record is being played at the wrong speed
2. Tracert to something like CNN.com is fine when making the hop from the workstation to the router, but once it goes out of the modem to the DNS we start to see lost packets and timeouts.  No tracert completes
3. When we try to check 'internet' speed, the system on Cox's end reports an error that it can't determine the network speed
4. Rebooting the modem does nothing
5. RDP-ing to systems behind my router is impossible because of network latency

They happen randomly at least once a day and sometimes cable goes out with it. I could be working or watching a you tube video or not even at the pc and suddenly everything just stops working  and I look at the pc if i am not their and see things are having to reconnect like yahoo messanger or work apps and I jump on to check and no websites work usually clears up after 10 to 15 minutes but while working kind of messes everything up.  When its working it works fine but the hiccups make it hard to call you guys and pin down an issue becasue it clears up. 

yeah and when they are here its working so they dont do anything.  Unless someone sits and watches the connection it will never be fixed. 

On and off issues all morning today so far. Tried to chat with support and everything stopped working. Modem lights didnt change till it went down about 20 minutes ago this time the modem lights turned off and on.