It is a bug between the TC and later Mac OS.. it has been there since Lion and still isn't fixed.. Apple spend all their programming effort now on your ipad and iphones. as they are highly profitable.. much less on the computer and network side of the business.. !! So enjoy the occasional reboot.. daily.. put it on a clock timer and force a reboot at midnight just before it goes pumpkin like.
An external drive is much more reliable.. the issue has to do with network connection and loss of something.. although I am sorry I cannot tell you exactly what. The computer is still connected, still works on internet but has actually lost the hard disk.. lost and cannot find it without a restart.
If you want to try a few changes it can help.
1. If you are connected by ethernet make sure wireless is off in the imac.. having only one network connection is better than two.
2. Redo the TC setup with all short names.. no spaces.. pure alphanumeric. Apple has these long names with spaces and characters like apostrophe by default but they are not a help.
3. If the TC is the main router then reduce the dhcp lease time.. make it 20min.. that keeps everything refreshed and up to date.
None of those fix it but they may help stretch out the interval.
I thought that reducing the DHCP lease time would increase the frequency of IP address renewing, and at the same time increase the number of opportunities to get the problem. May be I just misunderstood. Can you explain how it helps to strech the interval of occurences?
I have a similar problem and I am very interested by your expertise. See my post here: