I'm no network guru either but by a very painful 3-day process of elimination (when I should have been doing DIY projects! - wife not happy), I found a solution that works for me so far. Although, there is one test to do - whether it will last more than 24 hours!
I had - iPad, iPhone, iMac, wireless printer. My iMac uses ethernet to a small netgear switching router which is connected to my powerline ethernet. The powerline ethernet goes downstairs to another powerline ethernet that my Airport Extreme is wired to. My Airport Extreme is a wireless extension of my Airport Express. My Airport Express is linked via ethernet to my O2 wireless router.
I know that's complicated but I'm in an old Victorian house with thick walls and lots of steel, iron and plaster, it's complicated.
I eventually tracked down the problem to definitely being between the router and my iMac. Every time I turned on my iMac or shutdown, I'd loose internet connection on my iPhone and iPad - they can see the local network but not the internet. So the router isn't letting them 'leave the building' to go find the internet. Maddening.
It was also just turning off the internet conneciton on my iPhone and iPad randomly when the iMac was on all day - not just on boot up and shutdown.
They'd only work if I turned on and off my router every 15 mins or so. Drove me crazy.
So it had to be an IP problem. It's the only thing I could think of. I switched my iPhone and iPad to just connecting to the O2 router - still nothing. So it wasn't my Airport network causing the issue.
My iMac was connected the internet every time.
So - it's definitely to do with the DHCP lease.
I changed the IP address Using DHCP iwth manual address. But then lost all internet connection not only on my iphone and ipad but now my iMac too. Silly me - because of course, you have to tell your router that you are changing it to a static address too.
I also changed IPv6 to local link only in case that was causing issues (I can't think why it would but it was some positive action I could take). And I changed the location to Automatic in case that was having an issue too. Again, can't think why it would but anything at this stage was a possibility.
So far, so good. I'll keep you posted. But I'm so keen to solve this maddening problem I'll stay up all night if I have to. I'm also so maddened by it, I really want the world to know when I have a solution so they don't have to go through the same thing!
Apple - just tell every one a fix - Please!!!!!