Would a new modem solve this?

Hi everyone,

I was wondering if a new modem, like this one:
http://www.amazon.com/ARRIS-SURFboard-SB6141-DOCSIS-Cable/dp/B00AJHDZSI?psc=1&SubscriptionId=AKIAJM4NKIQGABP2PIRA&linkCode=xm2&camp=2025&creative=165953&creativeASIN=B00AJHDZSI&tag=thewire06-20&ascsubtag=WC12298, would solve my problems. Say I am downloading a game on steam, every 10 minutes or so of a sustained max download speed (around 2.5 megabytes per second) the internet cuts out for about 10-15 seconds. I have Time Warner Cable's turbo internet package, and a modem that has been in my house for years. There is a maximum of 10 devices connected at any time, but an average of 3-5. Can my modem not handle all the devices/data being pumped into my house? Does the amount of devices connected matter for a modem?

Also I do torrent quite often so this may be some limiting on the ISP side?