Gotcha.. Thanks for reminding me.
I think the issue has to do with the poor networking in Mavericks.
Your TC is now on the end of a long chain. It is actually invisible to the computer.. at least the hard disk is to Time Machine.
I have yet to explore the eccentricities of Mavericks.. in fact I have only just loaded it onto a poor laptop and ever since I rarely turn it on. But something is happening that is causing Mavericks to have multiple issues with network disks and especially Time Machine.
Let me suggest a work around.
I just turned the Wireless Network mode to off for the Time Capsule.
Turn the TC wireless back on. Set it up using all short names.. TC station name, as well as wireless.. no spaces and pure alphanumeric.
I recommend something like.. TCgen5 (or 4 or 3 whatever gen your TC is).
Wireless names.. yes use two.. one for each band. TC24ghz and TC5ghz.
Now instead of using the main wireless from your Unite.. use the TC wireless.. and if possible use the 5ghz.. it is much faster if you are within range.. otherwise use the TC 2.4ghz.
You will still get internet just fine. And although it is double hop wireless I doubt the speed is that fantastic to begin with.
You will then be directly connected to the TC.. and Mavericks will work much better.
Try it and yell if you find it is my hopeful imagination.. and a harsher reality.. because there is some more we can do.