There could be a couple of causes for this issue. Your internet could be degraded when it gets to your house causing disconnects. You will have to contact your Internet Service Provider in order to have them resolve this issue. Normally, they will replace splitters and may even replace lines outside of your house. You could also be having problems with the modem directly. The may replace this. You could also try to upgrade the software on it. Click here
for the update page for Arris.
Typically, I recommend you unplug the
router, plug the computer directly in the modem and see if you still
have the problem. If you still have the problem then you know it is just
the modem. If the problem resolves itself then you know the most likely
culprit is the router.
I would also recommend that you update your router firmware as well. Do a google search for the brand name of the router and go to the companies website, look in the support/downloads section for updated software.
--If possible, try a different Ethernet port on your router. You may have a bad port.
--Take out and reinsert all Ethernet cables on your network. Loose cables can cause disconnects.
--If possible, replace the Ethernet cables. Bad cables can cause this.
Lastly, you could be having an issue with the Network card(NIC) on your computer. Network cards are either built into the modem or external(a card you insert into the motherboard). Using the process of elimination and the steps above, you can hopefully narrow down the problem to one specific component of your network.
Let me know if you have any questions.