Hi - here's what I found was at fault with the situation I had that was similar - it involved the Apple TV box that permits ipad to do the Airplay mirroring trick to a big TV, but this fix ought to apply to any airplay device, as it is settings on the router that seem to be the problem - hence buying an expensive sophisticated router fixes it, or rebooting a router fixes it for a 25-minute spell, etc. Anyway read on for the general principle:
AIRPLAY solution shared by sleekitwan in various forums, eg Apple, BT:
Hi
First, before you lose interest - I have a solution that works so well to get BT Home Hub 3 working with 'Airplay' and Apple TV and my iPad 4, that I am so far unable to 'break' it. Please do try to break it yourself, and could you report back here or mark it with stars or whatever so I know what happened in someone else's setup?
I appreciate what you are going through, all I wanted to do was get 'Real Racing 3' running for me and the kidz on the TV that is attached to Apple TV box. Sometimes the Airplay icon appeared, sometimes not, it was chance - really frustrating.
The nub of it is this - you 'reserve' certain aspects of how the HH3 services the wifi network, so it directs data/communications via these 'reserved' ports specifically assigning them to the purpose you need - in this case, 'stuff' (technical eh?) going to the Apple TV so that Airplay works.
Apple forums somewhere list these publicised ports, and you go into HH3 management (tap in the IP address of the hub in 'safari' to get there, then put in your password for admin - it is 'admin' if you didn't change it already). In short, you use one of the games/applications that already are in the list for 'Port Forwarding', and I modified the name of a new one I made to make it like 'Airplay attempt using BT alarm' or something, because I 'copied' the BT safe alarm app details to start my custom one off. Lost yet?! Go into the HH3 manager, go to the A-Z I think it might be in 'advanced' and get 'Port Forwarding' up.
Ok, here's the things to set - if you peruse the apps/games they already list in HH3 for this sort of thing, you will see entries under 'TCP' or 'UDP' headings, and it's these sort of things we want to reserve. I only set the single specific addresses (it's just a number to you and me) that were listed on the Apple site as being to do with Airplay:
There are only 2 bits to set - you hit the button on screen in HH3 manager, to 'add entry', then select in the box marked 'protocol' that you want TCP or UDP according to the info I dug up from Apple site below - don't worry it is not complex to do you are just editing a couple of figures on a thing you don't use. Incidentally, I left the first two entries as they were (1024 was in there already) because I am just timid! So set it as below.
TCP 1024 -
UDP 1024 -
TCP 80 80
Any 123 123
TCP 443 443
Any 554 554
TCP 3689 3689
UDP 5353 5353
I took a pic of mine, for records, and this is what is in that pic. You have to enter the self-same number (eg 123 as above) no less than 4 times, this gives the results above.
On the bottom right, there is a button that says 'apply', so you hit that and it saves this new-fangled custom designed list of reserved ports/addresses for your 'Airplay BT alarm' or whatever you called it. THEN YOU MUST ASSIGN THIS CREATION OF YOURS TO A DEVICE - THE APPLE TV.
That's the basics of what I did - I have since restarted the BT HOMEHUB 3 several times, the Ipad 4 several times, the Apple TV has updated its software and has been restarted twice. STILL AIRPLAY WORKS.
So, I am reassuringly presented with the Airplay icon whenever I 'upswipe' on my ipad from the bottom of the screen - iOS 7.1 is on my ipad obviously, but that did not change the hit-and-miss of the Airplay icon until I made these mods to the HH3.
Over to you - try and break my solution please, and let me know if it works for you as well, or not. All I know is, Real Racing 3 can reliably be brought to bear on the Apple TV thing, and the Airplay icon is now never missing.
One more point - I think I also set the Apple TV IP address to be static - my ipad has had this situation for some time, along with the 'lease' set to a couple of weeks or something, so it does not try to select a different channel for wifi frequently? PLUS, I set something in the ipad I think, long ago (did not affect this issue as far as I can see), so that when the ipad 'wakes up' it does not decide to search for a better channel or IP address or something - that caused loads of glitches it seemed, then I found out my BT HH3 was on the end of dodgy phone cable not hi-quality shielded...but hey, that's a different bucket of bolts.
Good luck and let me know an outcome please, best to all.