What if the Jamestown settlers had been able to survive the Starving Time of 1609-1610? Could the colonists have created a permanent British settlement in Southern Mainland North America?
It's possible, but not likely in the short run-after the failure of Jamestown, many of the settlers who had already left the colony(because nobody who stayed would survive past April) ended up settling down further north, mainly to what eventually became the Maryland and Lenape of today's America: eventually, the English gave up trying to expand in that direction, and the Spanish essentially ran a lot of everything south of 36'30* for a good while: it wasn't until 1692, when the Scottish set up the New Argyle colony(later Georgia, and then known as Cherokia), that the English took interest in the southern areas of the Atlantic Seaboard.....a year later, a war erupted after the Spaniards tried to get some of the Chesapeake tribes to turn against the English, and the rest is history(i.e. the Spaniards lost and got booted all the way back to Florida).
Also, regarding the northern colonies? Well, it's certainly quite true that the moderate Puritans' colonies in what was to become Maine and New Hampshire(not to mention Plymouth!) fared well from the get go, yes, but not all was well up North, either; in fact, Massachusetts, by the latter 1680s, was starting to be in danger of falling apart itself, only thru major internal strife and the increasing repression from the governments in Boston, instead of starvation as with Jamestown. Hell, only after the Witch Trials of 1688 got out of hand, did outside intervention finally come and set things right(there's a reason why N.H.'s then colonial governor, J. Winthrop, is often regarded as one of the 200 Greatest Americans, after all).
If we're going to speculate on what a successful more southern English colony might have been like ITTL, the history of the Mass. Bay Colony would be a reminder of what not to do.