Time Capsule works with MacBook Pro (Mavericks) but not with IOS devices? recent problem starting March 1, 2015.

Question

I have a Time Capsule version 7.7.3 (model A1470) which has worked fine for almost 2 years with all devices, Apple and otherwise.  As of beginning of this month, March 2015 - no longer works with a new IPAD mini 3 and 6-month old iPhone 6 (both updated as of last night) BUT still works fine with MacBook Pro (Mavericks 10.9.5) and Epson printer XP-600. 
On both IOS devices Airport Utility shows the Time Capsule and shows green light connection to internet, but never does the connection. The little status circle just keeps going round and never shows the Wifi rainbow symbol. both devices work fine on other Wifi's.  Airport Utility on iPhone actually connects enough to check on Airport base station's firmware 7.7.3 and says it is up to date!  but sadly stays on LTE.
Have tried resetting, replugging etc...
Also, tried checking on updates.  Nothing shows in Airport Utility. When I try to go to see past updates ~/Library/Application Support/Apple/AirPort/Firmware to see if updated, there is no Airport in the Apple folder?
A mystery...

Answer 1

Reset the TC to factory and redo the setup. see details below.
Here is the typical list of things you should try.. and if this doesn't help post again.
Factory reset universal
Power off the TC.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the TC to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
N.B. None of your files on the hard disk of the TC are deleted.. this simply clears out the router settings of the TC.
Setup the TC again.
ie Start from a factory reset. No files are lost on the hard disk doing this.
Then redo the setup from the computer or perhaps it is better using iOS on the phone or ipad currently having issues.
1. Use very short names.. NOT APPLE RECOMMENDED names. No spaces and pure alphanumerics.
eg TCgen5 and TCwifi for basestation and wireless respectively.
Even better if the issue is more wireless use TC24ghz and TC5ghz with fixed channels as this also seems to help stop the nonsense. But this can be tried in the second round. For iOS the fixed channels particularly for 2.4ghz has helped.
2. Use all passwords that also comply but can be a bit longer. ie 8-20 characters mixed case and numbers.. no non-alphanumerics.
3. Ensure the TC always takes the same IP address.. you will need to do this on the main router using dhcp reservation.. or a bit more complex setup using static IP in the TC. But this is important.. having IP drift all over the place makes for poor networking. If the TC is main router it will not be an issue. This is a problem for a TC in bridge mode.
If this is of no help.. what modem do you have? What function other than modem does it have.. ie none or router??
How is the TC connected into the network? What function does it have? Router or bridge for example.
Post a few screenshots of the setup.