Time capsule losing internet connectivity (only with some clients)

Are the Roku units on ethernet?

Can you plug a computer into the TC by ethernet.. does it have internet connection?

Do you have ipv6 turned on to local link for the wireless devices? Probably irrelevant but just asking.

You are not alone.. lots of people are having issues with wireless in the new AC units..

My recommendation is to try again with clean setup.

Setup wireless with short names, no spaces and pure alphanumeric. Give a different name to 5ghz.

Only wpa2 personal security is up to the task .. do not use lesser values.

Use password of 10-20 characters pure alphanumeric.

Manually set the wireless channels.. try 1, 6, 11 for 2.4ghz and try around 40 and around 150 for 5ghz.. actual channel there is not a concern.. but one high and one low.

The apple devices are set up to Configure IPv6 Automatically, I guess this was the default.

Set to local link.. this is maybe going to help .. and maybe do nothing.

See http://support.apple.com/kb/TS4597

I did try changing to manual 5GHz name and channels, but upon trying to reset the station to apply changes, it froze up and I actually had to unplug it to get connected again.

Changing wireless via wireless is akin to sawing off the branch you are sitting on.. do all setup over ethernet.

I guess I'll try a hard factory reset. Any idea what happens to my time machine backups in that case?

Absolutely nothing will happen to your backups.. they are unaffected by resets of any type.. the only way to delete files is deliberately via finder or using airport utility to erase. Nothing else works.. so nothing to worry about.