Assuming you are are using DebugDiag 1.1. You need to use the correct version that matches the process architecture (there are 32bit and 64bit versions).
To check whether your application pool's worker process is 32bit or 64bit go to:
Control Panel -> Administrative Tools -> Internet Information Services (IIS) Manager
Don't open Internet Information Services (IIS) 6.0 Manager.
Open the Advanced Settings for your website (the link is on the Actions pane to the left). Note the Application Pool name then click Cancel.
Click on the Application Pools node on the left hand navigation tree pane and right click on the Application Pool noted above, select Advanced Settings.
If the application pool is 32bit then the setting Enable 32-bit Applications will be set to true, otherwise if false the pool will run in 64bit mode.
If the application pool is running in 64bit mode then you need to download and install the 64bit version of DebugDiag.
When you run 32 bit DebugDiag the column "32-Bit" on the processes tab will have "Yes" to indicate that a process is 32bit. Only these processes will have context menu options to 'Monitor For Leaks' and so on.
For more information see Tess Ferrandez's blog:
Capturing memory dumps for 32-bit processes on an x64 machine
If you can reproduce your suspected memory leak in 32bit mode then just switch the application pool to 32 bit and use the 32bit version of DebugDiag. Unfortunately both the 32bit and 64bit versions can't co-reside on the same machine.
Update:
DebugDiag 1.1 x64 only supports the
analysis features. There is a new
version in beta that does permit all
the functionality of the 32bit
version. Although not available
directly you can request a copy from
their support team, see the following
link for more info:
Debug Diag 1.2 (Beta)