When using TabBrowser Extensions (TBE) by Hiroshi (a popular extension for Mozilla Firebird), you need to turn off the clipboard option. Otherwise PowerPaste will not work, as TBE will paste every clip into itself. It uses a polling mechanism, instead of the regular clipboard notification chain, so it's not influenced by the "powerpaste shield" feature of ClipMate (PowerPaste Shield can't protect against TBE).
Here's how to turn it off:
If you go to Tabbrowser Preferences > Advanced Use, there's a checkbox at the bottom in the "Observation of Clipboard". Turn it off.
Thanks to Michael Klein, author of Download Wonder, for figuring this out.