I am getting the same problem - with an additional clue that half the time the Update button is partially concealed by the slider configuration box. The delete button does not work either but the Drag and Toggle links are OK.
I am getting a jscript error on the page (see text below). I have tried disabling other plugin (WordPress SEO) but it makes no difference. I am running WP 3.4.2 and slider version 1.2.0.
I don't know whether this is the same problem but would like to solve it as it is just the slider we need. I would prefer not to have to hack the post meta to get the extra slides in.
Any ideas gratefully received.
Webpage error details
User Agent: Mozilla/4.0 (compatible; MSIE 8.0; Windows NT 6.1; WOW64; Trident/4.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; .NET4.0C; BRI/2; MALC)
Timestamp: Tue, 25 Sep 2012 11:18:03 UTC
Message: Object doesn't support this property or method
URI: http:// /wp-content/plugins/cyclone-slider/js/admin.js?ver=3.4.2