It seemed that "forget this network" on the iPhone or iPad and re-establishing or releasing and renewing the IP on a Macintosh computer did the trick.
To me this was not a big deal. I had other priorities. Some of those who visited my humble abode, however, found this quite annoying and made quite a ruckus about it - to the point where I spent a whole week end testing things out and searching the web. (I didn't really need the whole weekend - it was an excuse to try out some new network equipment which was fun for a nerd.)
Finally found the culprit. The last update to the NETGEAR firmware has a bug.
To fix you can downgrade the firmware on your router.
Before you start login to your router and see figure out the current firmware for your router. Typically you can login at http://192.168.1.1. For my model the firmware version is on the advanced tab.
1. Go to Netgear.com
2. Click support at bottom of page
3. Click on for home
4. Click on Browse Products
5. Click on Routers, Modems & Gateways
6. Click on wireless routers & gateway modems
7. Choose your model.
8. Click Select
9. Under Firmware/Software your version likely matches the latest version. Click on Get More Downloads.
10. Scroll down and select one version prior than the one you have.
11. Download the file, unzip.
12. Find the tab in your router where you can select and choose that file to apply that version to your router.
Sadly, these downloads are not over SSL. HTTPS doesn't work on the download page. There is also no checksum to verify the contents of the file.
But hey, it fixed the problem for me.
Updates and patches are important for security, so keep an eye out for a newer version that lists this issue as fixed in the readme and continue to update at that point.