Script hangs after replacing a lot of regexp's in a very large string by sba

I wrote a script to "clean up" data from an application logfile that contains Unicode characters in the middle of an ASCII string.

The logic is as follows:

    while ($str -match '(.*)(Wstring={[^}]*\000[^}]*})(.*)')
    {
        $str = $matches[1] + ($matches[2] -replace '\000', '') + $matches[3]
    }

On a particular file, the script hangs (and the PowerShell host consumes CPU).