Would a new modem solve this?

Hi everyone,

I was wondering if a new modem, like this one:
Amazon.com, 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?