Windows shows "Limited Connection" when it isn't

Nice. You would have thought setting EnableActiveProbing to 0 would have the opposite effect.

This article explains exactly where the key is for. It can disable the probes to msftncsi.com which is to check if you have a good internet connection.

When a Windows machine connects to a network, there are two technologies, Network Location Awareness (NLA) and Network Connection Status Indicator (NCSI); it uses to automatically identify the network it is connecting to and whether or not it has access to the Internet.

It also explains why you have a “limited” connectivity icon (with all the problems that come with it).

Setting this value to 0 will disable active probes. A potential side effect is that, the machines may determine that they don’t have internet connectivity and display a or exclamation “!” on the network icon and “limited” connectivity in the network UI.".

In this case (if you have a good internet connection) setting it back to 1 would get rid of the “limited” connectivity.

There is probably some tool you used, that sets this to 0. When the problem occurs again, check the value, and if it's 0 again there is a tool that's doing it on the background.

Edit:

If you really don't want the check to msftncsi.com i think you need to set multiple options: (source)

1. Set the following key in the registry (as it was for you):
   HKLM\SYSTEM\CurrentControlSet\Services\NlaSvc\Parameters\Internet\EnableActiveProbing
   set it to: 0

2. Edit GPO (gpedit.msc for a local machine or gpmc.msc if AD domain wide):
   Computer Configuration > Administrative Templates > System > Internet Communication Management > Turn off Windows Network Connectivity Status Indicator active tests
   set to: ENABLE

3. Edit a second GPO:
   Computer Configuration > Policies > Administrative Templates > Network Connections > Do Not show the “local access only” network icon”
   set to: ENABLE

But if you can live with the checks to msftncsi.com i would leave them enabled.

For the really paranoid among us there is also the option of running your own NCSI-server
(explained here).

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Edit #2:

If there is a utility that's changing the value of EnableActiveProbing to 0 every couple of days (and you can't find it) you could create a EnableActiveProbing.reg on your Desktop and run it once you encounter the problem. (easier then digging through regedit.exe):

Windows Registry Editor Version 5.00

[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\services\NlaSvc\Parameters\Internet]
"EnableActiveProbing"=dword:00000001

And... even easier... you could create a batch-file that disables your "Local Area Connection", changes the registry key EnableActiveProbing back to 1 and enables the network connection again...
(i know, i'm lazy):

EnableActiveProbing_and_restart_connection.bat:

netsh interface set interface "Local Area Connection" DISABLE
REG ADD HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\NlaSvc\Parameters\Internet /v EnableActiveProbing /t REG_DWORD /d 1 /f
netsh interface set interface "Local Area Connection" ENABLE

I hope you find the culprit that is changing the key soon...