When one reaches the 1600s, many of the "natural philosophers" (we'd call them scientists today) of ancient Greece - I'm thinking Aristotle, Galen (anatomy), and Ptolemy (astronomy) as the best examples - start being questioned and revised. Aristotle spent a lot of time categorizing and defining the traits of animals and plants, and his taxonomy helped to inspire the modern classification system. Galen's notions of human anatomy were unfortunately false - it looks like the people of his time had the same taboo that medievals did about dissecting humans. Ptolemy also was incorrect in his idea the earth was at the center of the cosmos.

So throughout the 1600s, as part of the Scientific Revolution, this process goes on revising and improving on the ancients leading to the development of modern science. For instance we have Vesalius, who contradicts much of Galen, and the famous Copernicus, Galileo, and Kepler who contradict Ptolemy.

How does Aristotle avoid the same fate as Galen and Ptolemy and remain relevant to us? I would say this is due to his wide array of interests. Aristotle was many things. He was a literary analyst, ethicist, and political thinker (and so on) in addition to being a natural philosopher. While Aristotle's contributions to what we would call "science" may have been rendered obsolete, his other works are just as relevant today as when they were written. For example, his work on logic remains sound; his literary theory; his hylomorphism (the idea the soul is produced by the body - Aristotle was so controversial to medievals for this idea); his ideal of eudaimonia (happiness) being the product of virtue; his political theory; and so on.

Theophrastus may be of relevance to botanists, but would likely be falling victim to the same issue of "obsolescence" when it comes to the natural philosophers. There would simply be more modern writings that would be a better standard of where our current knowledge is. Otherwise, to maintain relevance he would need to have produced a range of works on other topics, like ethics and literature, and novel ones, on the scale of his teacher.

In regard to Socrates and Plato - these two were not natural philosophers so they do not run into the issue of "going out of date." They were dedicated to topics like politics, ethics, and metaphysics rather than botany or zoology. Socrates gives the august example of life, his dedication to virtue and truth, his elenchus (questioning method), and his trial, where he willingly gives his life in the pursuit of truth. He is the true father of "philosophy," the love of wisdom.

Plato is as complex a thinker as Aristotle, but where Aristotle is a "scientist," Plato is a "mystic." The famous painting of Raphael is a great example of this - in the center Aristotle points out to the physical world while Plato points up at the World of the Forms. To use just one work as an example, Plato is probably best surmised by the Allegory of the Cave; that man, either through ignorance or falsehood, is imprisoned, and the search for truth breaks one from prison and leads one to a higher reality (the world of the forms).