@Solla-topee 

Hello and thank you for replying to my query.

Yes the Kindle Fire (7th edition UK) is the only device that fails to connect now the TL-WA850RE is configured as an access point but it connected perfectly well when the 850RE was configured as a range extender.

I have tried re-booting the Kindle Fire several times and each time it fails to obtain the IP address of the 850RE.

As I mentioned in my original post, the Kindle Fire connects perfectly with the router WiFi and my Netgear range extender which is also configured as an access point. The encryption and security settings on all 3 setup's look to be the same, all of which were configured automatically.

I have also tried re-booting the 850RE a couple of times to see if that solved the issue, it didn't.

What I may try next is a re-set of the 850RE and start again, another idea is to remove the Belkin Powerline units and replace them with a temporary ethernet cable to the nearest wall outlet and see if that makes any difference.

Anyway, thanks again for taking the trouble to reply. It is much appreciated.  

@The-Driver 

Since replying to Solla-topee I have discovered that my old Samsung tablet no longer connects to the TL-WA850RE, I will investigate further.

@Solla-topee 

Hello again and sorry for the delay in replying, my time doesn't seem to be my own at the moment.

The Samsung tab and the Kindle still don't like the 850RE though my nearly new other Samsung tab and my IPhone have no trouble.

I am located in the north west of England and I think I've had the 850RE for about a year.

Sorry but as yet I've not had a chance to try eliminating the Belkin adapters, also I need to dig out my reel of cable and make up a 10 metre ethernet patch lead.

Here's hoping I get chance to make some progress before the end of the week.

Update.

I wanted to test the 850RE in situ with Ethernet provided via cable direct from my router but as that wasn't as feasible as I'd like I moved the 850RE to a location that already had Ethernet outlet close by and it worked fine, even with the Kindle Fire. 

This answers the what question but not the why, it also creates the question, do I pursue the issue and find out why the Belkin Power-line adapters are the issue and try and overcome the problem or do I simplify things and locate the 850RE a little further away than I'd prefer and provide a direct Ethernet connection. 

Okay, relocating the 850RE means some physical work but it will probably be easier than solving the technical issue with the Belkin units.