Unfortunately, we don't have much in the way of specific details that would help us try to figure out what the real issue here might be......things that you may have already done......but did not mention in your post.
Have you connected your computer directly to the modem for a few days to see if the Internet connection "holds" that way.....or.....whether the Internet disconnection issues still continue during the "test" period?
Have you had a technician from your Internet Service Provider (ISP) out to your house to inspect all of the wiring and connectors associated with the Internet line?
What is the make and model number of the modem? We ask this because there are some known compatibility issues between the Motorola/Arris SB series of modems and the newer 802.11ac models of the AirPort Extreme and AirPort Time Capsule.
Who is your ISP? Most ISPs are in the current process of implementing a new type of Internet connection called IPv6 into their current systems, which requires updates and changes on the system that are supposed to occur smoothly overnight.....but sometimes cause a loss of the Internet connection in the process. IPv6 implementation is going relatively smoothly for most ISPs, except one major player in particular that is having numerous documented issues with current Apple routers.
Finally, there have been some power supply stability problems on the newer AirPort routers, which cause a momentary intermittent loss of voltage resulting in a lost connection when the AirPort automatically restarts. This issue is very difficult to catch, since it occurs very briefly and you almost have to be staring at the AirPort at the time to know that it has occurred. If everything else checks out, it may be the AirPort router that needs to be replaced. I've had this problem personally, and the only solution was to replace the AirPort router.
