I had this exact problem with Time Warner Cable, a Motorola SB5101 modem, and the DLink DIR_655.
TWC came out and checked the cable signal and said everything was fine (as they always do). However, the problem continued to occur. So I contacted Motorola Tech Support and they had me access the SB5101 admin page (just enter the modem's IP address in your browser's URL box). Then click on the Signal button. The web page will display the downstream signal strength. In my case, it was -11 dbmV. While within spec for the SB5101 (-15 dbmV to +15 dbmV), Motorola Tech Support said they much prefer to see the number closer to zero.
The tech support guy asked if there were any splitters between the incoming line and the modem. In my case there was one to split the incoming signal between internet and TV distribution. He suggested I remove that and see if the problem went away. So as an experiment, I bypassed the splitter and re-measured the signal strength via the SB5101 admin page. The signal strength was now at -6 dbmV which means the signal was over 3 X stronger. With that change I had no more dropped connections. However, I also had no cable TV since I had eliminated the splitter.
So I purchased a cable booster with support for an internet connection (you have to be able to communicate upstream). Once installed, the signal strength to the SB5101 measured +6 dbmV, which means the signal is now 6 X stronger than when I started. And as an added better, I have a crisper picture on my TV's.
So it isn't necessary to buy another cable modem, just boost the signal strength to the one you have, and the dropped connectivity problem should go away.