Randolph remained active until 1913 according to my sources...
The company was swallowed up by GM in 1909 and I had multiple sources listing the last year of production as either 1908 or 1909. I suppose GM could have continued to produce vehicles under the brand for another year or so, but I was unable to find evidence of any Randolph-branded vehicles being produced after 1910 and wanted to respond as accurately as possible. Sorry!