You have two different threads with different answers..
But I would recommend you reset the TC to factory and start over. No files are lost doing this.
There is some more details I have included.. not all are necessary but do them one by one. If you cannot get it to work, more details of your whole network layout please.
Make and model of the main modem?? Some modems are unreliable with the AC version airports.. SB single port cable modems.. eg SB6141 being top cab off the rank.
ISP? It matters particularly with upgrade in cable to IPv6 and some ISP using poor implementations.
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.
Then redo the setup from the computer with Yosemite.
1. Use very short names.. NOT APPLE RECOMMENDED names. No spaces and pure alphanumerics.
eg TCgen5 for basestation and TCwifi wireless name.
If the issue is wireless use TC24ghz and TC5ghz with fixed channels as this also seems to help stop the nonsense.
2. Use all passwords that also comply with 1. but can be a bit longer. ie 8-20 characters mixed case and numbers.. no non-alphanumerics.
3. If the TC is main router you can skip this point. This is only an issue when the TC is bridged.
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 gives poor reliability
4. Make sure IPv6 is set to link-local only in the computer. For example wireless open the network preferences, wireless and advanced / TCP/IP.. and fix the IPv6. to link-local only. Do the same for ethernet if you use it.
There is a lot more jiggery pokery you can try but the above is a good start.. if you find it still unreliable.. don't be surprised.