How to change browser mode in IE9 permanently?

I don't think you can really affect the browser mode setting; this seems to be a developer debugging feature. If a user is running IE9, the browser mode will be IE9 or IE9 Compatibility View. You can affect the compatibility view setting by using the X-UA-Compatible <meta> tag or HTTP header (though, watch out for the Tools -> Compatibility View settings - > "Display Intranet sites in Compatibility View" setting).

I found a registry setting that can force IE9 to run in IE8 or IE7 in browser emulation mode permanently. For example, to run IE9 in IE8 mode, add the follow key, value, and data to the registry.

HKEY_LOCAL_MACHINE (or HKEY_CURRENT_USER)
   SOFTWARE
      Wow6432Node (for IE 32-bit on a 64-bit OS)
         Microsoft
            Internet Explorer
               Main
                  FeatureControl
                     FEATURE_BROWSER_EMULATION
                        iexplore.exe = (DWORD) 00008888

You can use decimal value 8000 for IE8, but is only applied if !DOCTYPE directives are displayed in IE8 mode. Decimal value 8888 is for IE8 regardless of !DOCTYPE directives, which is why I chose in my example.

Decimal value 7000 is for IE7, but only applied if !DOCTYPE directives are displayed in IE7 mode.

http://msdn.microsoft.com/en-us/library/ee330730(v=vs.85).aspx#browser_emulation

Note: The developer toolbar will display "Browser Mode: unknown", so that is not a valid test.

You can solve this issue with <meta x-ua-compatible /> element and providing it the ie7 variable.
Another alternative is to change the document mode using the documentMode property.
MSDN Reference:
http://msdn.microsoft.com/en-us/library/cc196988(v=vs.85).aspx