Although you do not say what operating system you are using, I will assume that you are at least using Internet Explorer 6 (IE6) for a Web browser. If that is the case, then try adding the URL of your Exchange Server to the browser's Trusted Sites list. Find this in the IE properties under the Security tab.
Also, it would be helpful to know if the problem is user-specific (i.e., it follows certain users from computer to computer), or whether it is computer-specific (i.e., it happens to any user at a given computer, or only to a certain user at a certain computer).
MEMBER FEEDBACK TO THIS ASK THE EXPERT Q&A:
This is a known Internet Explorer 7 and OWA issue. My coworkers who installed Microsoft Vista have experienced this problem.
I found valuable troubleshooting tips in this discussion thread at Microsoft's TechNet forum: "Outlook Web Access -- unable to use reply"
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Related information from SearchExchange.com:
This was first published in February 2007