Jamestown was established in 1607 what was then the Virginia colony and it most assuredly did survive, if only barely. It remained the capital of the Virginia colony until 1699, when the capital moved a bit up the river to Williamsburg.
Jamestown thus predates Plymouth by some 13 years as the oldest permanent English-speaking colony in North America.
I have 2 different 14th great grandfathers who arrived in Jamestown before 1615. One is John Rolfe, who married Pocahauntas.