Time Capsule: Problem connecting to the Server

Question

Specs:
MacBook Pro (Retina, 15, Late 2013), 2.6 Ghz Intel Core i7, 16GB 1600 MHz DDR3, NVIDIA GeForce GT 750M 2048MB, 1TB SSD, OSX Mavericks 10.9.4 (13E28)
Time Capsule 2013, 3TB, Firmware 7.7.3
"There was a problem connecting to the server "Xxxxx's Airport Time Capsule".
Check the server name or IP address, and then try again. If you continue to have problems, contact your system administrator."
I can access my Time Machine, but I cannot backup. Everytime I try to I get the above message. I had this problem in the past, but opening Time Machine System Preferences and Selecting and deselecting the current disk seemed to fix it. It was an odd fix, but every time I went into the settings to get to the bottom of the problem it resolved itself before I could get to the bottom of the issue. I thought I was imagining it at times! The Time Capsule is also giving my network sporadic connectivity issues to the internet. It will maintain a perfect wireless connection, but not provide a connection to the internet. Turning my notebooks WiFi on and off seems to resolve the issue upon reconnection.
What's going on and how do I fix it!
I also have AppleCare for the Time Capsule and would like to not get too crazy or involved with the solutions. Nothing that voids the warranty!

Answer 1

We would not suggest warranty voiding fixes on any device that has warranty.. we only suggest those when Apple refuse to help or the device is older.
Reset your TC to factory.
The Factory Reset universal
Unplug your TC/AE. Hold in reset. and power the TC/AE back on..  all without releasing reset and keep holding in for about 10sec. The time is not important.. it is the front LED rapid flashing that indicates you are in factory mode.
Release reset.
If it doesn’t flash rapidly you have released reset at some point and try again.
Be Gentle! Feel the switch click on. It has a positive feel..  add no more pressure after that.
TC/AE will reboot after a couple of minutes with default factory settings and will wipe out previous configurations.
No files are deleted on the hard disk.. No reset of the TC deletes files.. to do that you use erase from the airport utility.
Redo the setup of the TC.. using all short names.. with no spaces and pure alphanumeric.
Apple changed Mavericks default network protocol to SMB and it has tighter rules.
eg.. A good name is TCgen5
A good name for the wireless is TCwifi
Use whatever you like.. up to max 20 characters but short and sweet is better.
Once you do that, mount the disk in finder manually.
Go, Connect to server.. From the top menu area.
AFP://TCgen5.local
OR even better use its IP address.
AFP://10.0.1.1 (but it must be static which usually means in router mode).
Once you have found the network resource.. put in your disk password and save it to the keychain. All passwords should be pure alphanumeric mix of case and numbers and 10-20 characters.
Reset Time Machine to the new path to the TC.
It will say it will start a new backup but in fact it will discover the old one and simply continue the backup.
If it still fails.. it is faulty and should be returned.
The drop out of the internet even when wireless is working points to faulty WAN connection which is a serious bug on these.