No, there is no property of the control for the border itself and it should not disappear. This smells like an old issue of the input.
I tried something like that with an older versions of Telerik.Web.UI since I'm testing with the latest pre-release build generally but could not reproduce it unfortunately. Can you please post a sample code which replicates that? Would you also try if you get that both in IE or Firefox for example? I guess you get it on IE only, don't you?
the Telerik team