This looks like a bug.  When I have a simple LinkItemCollection property in my page or block content item, I cannot remove more than one link at a time in IE10.  It works fine in Firefox 31, however.  I have tested such a property in both a block and a page content type. My block property looks like this:

        [Display(
            Name = "Content List",
            Description = "Collection of content manually set via the CMS",
            GroupName = SystemTabNames.Content, Order = 30)]
        public virtual LinkItemCollection ContentList { get; set; }

When in edit mode for the content item using IE 10, if I remove more than one item in the list using the drop-down menu for each item (see screenshot below), they are removed as expected while still in edit mode, but as soon as I publish the change, all links except the first to be removed re-appear.  Please can you try to reproduce and if so confirm that it is indeed a bug?