Random D/C on modem

Hi so i'm with rogers I got the high speed I have to hooked up to a router linksys. So that me and someone else can use at sametime. So there is a problem with the modem I get randomly d/c it will happen maybe once or twice an hr it lasts for about 5mins upwards to 1hr sometimes the duration of the day. When it happens I check the modem and the cable light stops blinking then I reset it and it takes awhile to get connected again. I don't think the router is the problem because I can log into the routers setup. I think the problem might be the cable splitter is there any known problems with cable splitters. Its hooked to the TV and I also have rogers cable for tv. This gets really annoying if i'm doing a raid. Is anyone else also having this problem?? And I called rogers a few times they came over one time and said the cable phone I had before was the problem. I dont have it anymore and I dont wanna call them so I have to be on hold for 1hr or more. Also someone else told me to get a small ADJUSTABLE cable amplifier. And I get that the I.P address is in use already/conflict also limited connectivity. If you need any more info I can provide