This is because you are using Iron Portable - in which case you should not let Iron set its own file associations. If Iron sets its own file associations - they will go to Iron.exe and not IronPortable.exe. If you run Iron.exe - it will load a fresh configuration from the UserProfile instead of from the local IronPortable path.
You need to manually set associations. The following scripts sets associations manually for .HTML, .HTM, .MHT, and .URL. To use - copy-pasting the script into Notepad, change all path references to IronPortable.exe to the correct path, save the file with a .REG extension, and then right click the .REG file and select "Merge".
Windows Registry Editor Version 5.00
---------------------------------------------------------------
[-HKEY_CLASSES_ROOT\.html]
[HKEY_CLASSES_ROOT\.html]
@="MyHTMLFile"
"Content Type"="text/html"
[-HKEY_CLASSES_ROOT\.htm]
[HKEY_CLASSES_ROOT\.htm]
@="MyHTMLFile"
"Content Type"="text/html"
[-HKEY_CLASSES_ROOT\.mht]
[HKEY_CLASSES_ROOT\.mht]
@="MyHTMLFile"
---------------------------------------------------------------
[-HKEY_CLASSES_ROOT\MyHTMLFile]
[HKEY_CLASSES_ROOT\MyHTMLFile]
@="IronPortable MyHTMLFile"
"URL Protocol"=""
[HKEY_CLASSES_ROOT\MyHTMLFile\DefaultIcon]
@="T:\\IronPortable\\IronPortable.exe,0"
[HKEY_CLASSES_ROOT\MyHTMLFile\Shell]
[HKEY_CLASSES_ROOT\MyHTMLFile\Shell\Open]
[HKEY_CLASSES_ROOT\MyHTMLFile\Shell\Open\Command]
@="T:\\IronPortable\\IronPortable.exe --new-window \"%1\""
;---------------------------------------------------------------
[-HKEY_CLASSES_ROOT\.url]
[HKEY_CLASSES_ROOT\.url]
@="InternetShortcut"
;---------------------------------------------------------------
[-HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut]
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut]
@="Internet Shortcut"
"EditFlags"=dword:00000002
"IsShortcut"=-
"NeverShowExt"=""
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut\CLSID]
@="{FBF23B40-E3F0-101B-8488-00AA003E56F8}"
[HKEY_CLASSES_ROOT\InternetShortcut\DefaultIcon]
@="T:\\IronPortable\\IronPortable.exe,0"
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut\shell]
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut\shell\open]
"CLSID"="{FBF23B40-E3F0-101B-8488-00AA003E56F8}"
"LegacyDisable"=""
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut\shell\open\command]
@="rundll32.exe shdocvw.dll,OpenURL %l"
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut\shellex]
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut\shellex\ContextMenuHandlers]
[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\InternetShortcut\shellex\ContextMenuHandlers\{FBF23B40-E3F0-101B-8488-00AA003E56F8}]
@=""
;---------------------------------------------------------------
[-HKEY_CLASSES_ROOT\http]
[HKEY_CLASSES_ROOT\http]
@="URL:HyperText Transfer Protocol"
"EditFlags"=dword:00000002
"Source Filter"="{E436EBB6-524F-11CE-9F53-0020AF0BA770}"
"URL Protocol"=""
[HKEY_CLASSES_ROOT\http\DefaultIcon]
@="T:\\IronPortable\\IronPortable.exe,0"
[HKEY_CLASSES_ROOT\http\shell]
@="MyHTMLFile"
[HKEY_CLASSES_ROOT\http\shell\MyHTMLFile]
[HKEY_CLASSES_ROOT\http\shell\MyHTMLFile\command]
@="T:\\IronPortable\\IronPortable.exe --new-window \"%1\""
[HKEY_CLASSES_ROOT\http\shell\MyHTMLFile\ddeexec]
[HKEY_CLASSES_ROOT\http\shell\MyHTMLFile\ddeexec\Application]
@="ddeexec-http"
;---------------------------------------------------------------
[-HKEY_CLASSES_ROOT\https]
[HKEY_CLASSES_ROOT\https]
@="URL:HyperText Transfer Protocol with Privacy"
"EditFlags"=dword:00000002
"Source Filter"="{E436EBB6-524F-11CE-9F53-0020AF0BA770}"
"URL Protocol"=""
[HKEY_CLASSES_ROOT\https\DefaultIcon]
@="T:\\IronPortable\\IronPortable.exe,0"
[HKEY_CLASSES_ROOT\https\shell]
@="MyHTMLFile"
[HKEY_CLASSES_ROOT\https\shell\MyHTMLFile]
[HKEY_CLASSES_ROOT\https\shell\MyHTMLFile\command]
@="T:\\IronPortable\\IronPortable.exe --new-window \"%1\""
[HKEY_CLASSES_ROOT\https\shell\MyHTMLFile\ddeexec]
@=""
[HKEY_CLASSES_ROOT\https\shell\MyHTMLFile\ddeexec\Application]
@="ddeexec-https"
;---------------------------------------------------------------