Have you checked whether you have a network  connection from the TV? I seem to have lost mine since the update. WLAN as we'll as LAN. Have not tried to unplug the TV though. Needless to say all other devices I have can connect to the network. 

Hadn't thought of Bonjour, but I ran the test, and I have
_beoconfig._tcp

_beocore._tcp

_beoremote._tcp

and of course all the others that belong to other devices.

Yours resolve to the correct ip (which is static and dished out by DNS on the router, based on the MAC address) 

For the avoidance of doubt, I'm using an iPhone6.  
I get the same lack of response on an iPad mini

All right up to date 

Okay, that is strange.

When using the "Discovery" app, you will see the hostname string with the corresponding port on the first row.
Should be something like "BeoVision-Avant-55-0000000.local.:8080" 

Can you copy this into your iPhone Safari browser and see whether a page with some lines of text gets loaded?

If this is the case to communication from your phone to the TV is working.

Well, we make progress, of sorts.

Taking the string from _beoconfig it actually returns beovision-avant-55-24152911.local:1

That string in Safari returns nothing. If I edit it be port 8080, as you hinted, I get 

{"services":[{"name":"BeoNotify","path":"BeoNotify/"},{"name":"BeoContent","path":"BeoContent/"},{"name":"BeoDevice","path":"BeoDevice/"},{"name":"BeoOneWay","path":"BeoOneWay/"},{"name":"BeoInput","path":"BeoInput/"},{"name":"BeoZone","path":"BeoZone/"},{"name":"BeoSecurity","path":"BeoSecurity/"},{"name":"Ping","path":"Ping"}]}

So, it 'looks' as the the Bonjour resolver is returning the wrong port. Why, I can't answer! 

Well, we make progress, of sorts.

Taking the string from _beoconfig it actually returns beovision-avant-55-24152911.local:1

That string in Safari returns nothing. If I edit it be port 8080, as you hinted, I get 

{"services":[{"name":"BeoNotify","path":"BeoNotify/"},{"name":"BeoContent","path":"BeoContent/"},{"name":"BeoDevice","path":"BeoDevice/"},{"name":"BeoOneWay","path":"BeoOneWay/"},{"name":"BeoInput","path":"BeoInput/"},{"name":"BeoZone","path":"BeoZone/"},{"name":"BeoSecurity","path":"BeoSecurity/"},{"name":"Ping","path":"Ping"}]}

So, it 'looks' as the the Bonjour resolver is returning the wrong port. Why, I can't answer! 

Sorry, maybe it was me misunderstanding.

If I pick up the string from _beaoremote, it DOES have port 8080

Sorry, maybe it was me misunderstanding.

If I pick up the string from _beoremote, it DOES have port 8080

Okay, everything works as it should.

Communication is up an it seams that nothing gets blocked by your local network.
This is in fact what BeoRemote uses to discover the TV's. Looking for the bonjour service and starting communication over port 8080. 

Have you ever tried to delete and reinstall the app?

Can you check whether the name of your TV has an "space" character at the end?
Accessible via the network settings menu on TV.  
If yes, delete it and restart the TV. 

No space on the name.

Deleted and re-isntalled, this time, I got a 'tap and hold to select'.  I did this but nothing happened, and at some stage I got to the 'No products'. I exited, Next time I didnt get the option to tape and hold. Killed the app. Same result, so I deleted, re-isntalled- and got the tap and hold to select.  Same result. tried it about 5 times and then suddenly I got the Avant offered to me!

Played a little - worked. 

Closed the app - went back to it, and I am back to the 'no products'.

Type this message, wake phone up to double check, and this time I do get the Avant and it's menu.
The phones Wifi is rock solid - I get 4ms ping, 60Mb up, and 19Mb down, all day every day. The TV is hard wired, so it should be getting better performance.

Progress, definitely..