Strange redirects for Safari iPad only

I'm having the most weird thing happening with my web server. It's Apache 2 with SSL. To simplify, here's why my config looks like (example.com refers to my own domain, of course):

<VirtualHost *:80>
    ServerName example.com
    ServerAlias www.example.com

    Redirect 301 / https://example.com/
</VirtualHost>

<VirtualHost *:443>

    ServerName example.com

    DocumentRoot /var/www/example

    ... #options and allow/deny for directories

    ... #logging settings

    SSLEngine on
    ... #ssl settings

</VirtualHost>

<VirtualHost *:443>
    ServerName www.example.com
    Redirect 301 / https://example.com/

    SSLEngine on
    ... #ssl settings

</VirtualHost>

Essentially, what it does is redirect all non-https traffic to https and redirects www.example.com to example.com - so far, so good.

This works for all browsers on all platforms - with one exception: Safari on iPad. Safari on mac works fine; other browsers on ipad work fine, but on Safari on ipad I get "Safari cannot open the page because too many redirects occurred".

Now, the only redirect I have in my setup (on https) is from www.example.com to example.com. I added %{Host}i to the access log - and I can see that the requests contain correct hostname and resource.

At this point I am completely stumped. I don't know where or what else to look at. My client mainly uses ipads, so ignoring it isn't an option.

Any ideas are greatly appreciated.

EDIT:

I changed the SSL configuration to this:

<VirtualHost *:80>
    ServerName example.com
    ServerAlias www.example.com

    Redirect 301 / https://example.com/
</VirtualHost>

<VirtualHost *:443>

    ServerName example.com
    ServerAlias www.example.com

    DocumentRoot /var/www/example

    ... #options and allow/deny for directories

    ... #logging settings

    SSLEngine on
    ... #ssl settings

</VirtualHost>

Now there are no redirects in the config at all. I cleared all settings, history and stored data from the ipad - and it's still redirecting!