In addition to Bob's comments, I have the following two items to offer:
- A number of major ISPs have been rolling out IPv6 ... with mixed results, when it comes to Apple base stations. One workaround is to reconfigure your Time Capsule to use the "Link-local only" option for IPv6. This has had fairly good results in stabilizing the connectivity issue.
- The other is to see if there is an incompatibility between your Arris modem and your Time Capsule.
To change the IPv6 configuration of your AirPort base station you would need to use the AirPort Utility, as follows:
From a Mac:
- Run the AirPort Utility.
- Select the base station, and then, select Edit.
- Select the Internet tab, and then, select Internet Options...
- Change Configure IPv6 to: Link-local only
- Click on Save, and then, click on Update.
- Allow the base station to restart.
- Do this for each of your base stations.
From an iOS device:
- Tap on the AirPort Utility to run it.
- Select the base station.
- Tap on Edit.
- Tap on Advanced.
- Tap on IPv6.
- Change Configure IPv6 to: Link-local only
- Tap on Done.
To test for incompatibility, we are going to check the ARP cache. It should only contain around a dozen entries or so, but is somewhat dependent on the number of devices on your network. Basically it is a list of your current networking hardware. Considerably more entries could potentially indicate an issue.
We will use OS X's Network Utility to check the ARP cache, as follows:
For pre-OS X El Capitan:
- Run the Network Utility > Netstat tab > Select the option "Display routing table information" > Click on Netstat
For OS X El Capitan:
- Apple Menu > About This Mac… > System Report > From the System Information tool menu > Window > Network Utility > Netstat tab > Select the option "Display routing table information" > Click on Netstat

After selecting Netstat, it may take a few seconds to run. The end result will be a listing of ARP query entries for your local network. It should include any routers, and your network clients. For now you can ignore (don't count) the entries under Internet6. Again, you are looking for excessive entries. For example, in my case I have a router, three wireless access points and about a dozen clients. Netstat gave me around 25-30 entries