How could the flat earth theory survive

I thought no one believed the earth was flat after, well, after they really started thinking about it all, during the classical Greek age.

'Nobody' means the educated few.

The Church wasn't the sole repository of information but what information it did have it used to control the populace...

I think anyone who was susceptible to logical arguments would have already realised the earth was round. So only those who were swayed by dogma would have needed an explanation, and even then probably not a very good one.

"Earth's circumference was estimated around 240 BC by Eratosthenes, who knew about Syene (now Aswan) in Egypt where the sun was directly overhead at the summer solstice and used geometry to come up with a circumference of 252,000 stades, which, depending on the estimate of the unit stadia, is within 2% and 20% of the actual circumference, 40,008 kilometres."

http://en.wikipedia.org/wiki/Flat_Earth

At the time, very, very few people have a scientifical knowledge.
An educated people of the sisteenth century was studying essentially theological books, and greek classical ones.

Science has beggining to explode in the nineteenth century.

Believed, Shetline, believed, the guy is dead now.

On a side note, psychiatric hospital are full of people believing, they are Napoleon, Cesar, Alexander the great, an alien coming from the outer space ...

As mentioned above, an inertia of learning had much to do with it, associated to the strict control to which knowledge was subjected.
As this is discussed within the context of western and central Europe btween the yeas 500 and 1500, the subjects of the Earth's shape and of its place in the universe, were of interest of a few people even among the educated few. Those few were in the classical languages (mostly Latin), and dealt more with the supernatural than the natural sciences.
Between 1400 and 1600, spoken languages started emerging as languages of literature and, more importantly, of higher learning; books became more accessible as they were written in live languages rather than dead ones, and books were more affordable once they were printed. So suddenly there were more people thinking about those matters, disturbing the intertia.
And then there was the matter of maritime expeditions, driven by political and mercantile ambitions and fueled by the spread of learning and of curiosity.
Previously, when a ship ventured beyond the confines of the known world, the knowledge of it was kept very secret by whichever authority controlled the ship (this was also prevalent in ancient times, which is why it remains unclear just how far did the Carthaginians go).
Now, despite the intent to keep these things secret, the knowldge of maps, charts, and sea routes could not remain under such tight control for long.
So, after ships had sailed around the world, it had become common knowledge wherever knowledge was common.

So, the notion of the flat earth, followed by that of a geocentric universe, were discredited for all reasonable and learned people, though still commonly held by the illiterates and by a few literates who were (some still are) persuaded it is all a somber machination by powerful interests who supposedly exert tight control over knowledge.
Such tight a control, for reasons mentioned above, cannot be exerted outside of a very authoritarian setting where the authority uses raw and naked power in order to maintian itself and its control. Flat-eathers don't realise the shape of society had changed since the mediaeval times they so cherish and imagine their rivals to be a mirror image of themselves (or rather of how they wish they were), as absolute rulers over how knowledge is acquired and disseminated.

As could be expected, authoritarian regimes have their own variants of flat-earthers prevailing for a while over actual science, like Lyssenkoism and the such.

In our relatively open societies, proponents of such theses (more often than not, those are also proponents of a stricter society when they don't challenge the very foundations of said openness) can freely peddle their wares , and through some political circumstances they may even gain some notable influence, but for their theses to be able to prevail they must first gain the ability to exert absolute, raw, and naked power.

Simple. The flat earth theory was not really a scientific theory, it was a philosophy. The difference is that theory is a model made to explain physical phenomenon. The theory is tested by experiments to see if the theory is good enough to predict new phenomena based on understanding of old ones. If it's not, it is thrown out and a new theory formed.

Philosophy is a model of external physical or non-physical phenomena that is never tested by experiment. Most of the "theories" back then were philosophies. People simply believed even though they knew there were incosistencies within the philosophy itself!

Aristotle, for example, was a great philosopher, but a poor scientist. He never really tested what he believed in.

Think about religion. It's a form of philosophy and is still very powerful today despite that it has been proven inaccurate at describing physical world countless times.

Heh... a flat earth is the "plane truth"...