WordPress/Apache problem

We currently have several installations of wordpress 2.6.2 and 2.61 that worked perfectly until about two days ago.

Suddenly, when we are logged in as an admin and try to save a post we get the following error message:
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Forbidden

You don’t have permission to access /wp-admin/post.php on this server.
Additionally, a 404 Not Found error was encountered while trying to use an ErrorDocument to handle the request.

Apache/1.3.37 Server at aliceinparis.net Port 80
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We have not made ANY changes to the server setup/database authorizations.
The problem occurs in an identical manner on three separate installations of WordPress.

Basically, what happens is that we paste a long-ish text (1000 words) into the wordpress window, exactly as we did successfully with previous posts, and when we try to save we get this message, despite being logged as the principal wp admin.

Even stranger: when we paste only a couple of paragraphs, no error message appears. Nor does the problem appear when we create text inside wordpress, by typing directly into the text-edit window.

Any ideas?

Thanks!