IMac Continually Dropping WiFi Connectivity

Question

Due to appalling wired "broadband" where I am, I have to connect by tethering an iPhone 5 over an HSDPA cellular connection. That's all fine.
The trouble is that my late 2012 27" i7 iMac keeps losing connectivity although it continues to be - apparently - connected to the iPhone. Symptoms include no Internet connectivity, dropped connections to the Apple TV, etc.
None of my other equipment is affected, so it's not an overall connectivity issue, just with the iMac.
Is this a widely known problem?

Answer 1

Back up all data before making any changes.
Step 1
Take all the applicable steps in this support article. If you're running OS X 10.8.4 or later, run Wireless Diagnostics and take the remedial steps suggested in the summary that appears, if any. The program also generates a large file of information about your system, which would be used by Apple Engineering in case of a support incident. Don't post the contents here.
Step 2
Run Software Update and install all available updates for OS X or your computer's firmware.
Step 3
If you're not using a wireless keyboard or trackpad, disable Bluetooth by selecting Turn Bluetooth Off from the menu with the Bluetooth icon. If you don't have that menu, open the Bluetooth preference pane in System Preferences and check the box marked Show Bluetooth in menu bar. Test. Continue if you find that Wi-Fi is faster with Bluetooth disabled.
From that same menu, select Open Bluetooth Preferences. If the box labeled Discoverable is checked, uncheck it. Click the Advanced button, and in the sheet that opens, uncheck the top three boxes, if any are checked. Click OK. Enable Bluetooth and test again.
If the application called "Bluetooth Setup Assistant" is running, quit it. Note: this is not applicable to OS X 10.9 or later.
Step 4
This step will erase some of your settings in the Network preference pane. Make a note of them before you begin, and recreate them afterwards. It may be helpful to take screenshots of the preference pane.
Triple-click the line below on this page to select it:
/Library/Preferences/SystemConfiguration/com.apple.airport.preferences.plist
Right-click or control-click the highlighted line and select
Services ▹ Reveal
from the contextual menu.* A folder should open with "com.apple.airport.preferences.plist" selected. Move the selected item to the Trash. You may be prompted for your administrator password. Recreate your settings for Wi-Fi in the Network preference pane.
*If you don't see the contextual menu item, copy the selected text to the Clipboard by pressing the key combination command-C. In the Finder, select
Go ▹ Go to Folder...
from the menu bar, paste into the box that opens (command-V). You won't see what you pasted because a line break is included. Press return.
Step 5
Reset the System Management Controller.
Step 6
Make a "Genius" appointment at an Apple Store, or go to another authorized service center.