I need to restart cable modem every 10 days or so because my speeds reduce to a fraction of what I pay for. They say it's a modem problem... please mansplain in detail!

I'll translate Bruce's ridiculously long and ego ridden reply for you:

[translation]

It's your fault!

Your cables are loose so check them!

Connect a computer directly to your modem bypassing your router using a cat cable and run a speed test!

Check your modem logs!

[/translation]

What modem are you using? Can you post the signal levels as well as the modem logs to this forum?