Most (if not all) languages change continually. There's no reason why Latin should be an exception but, if you want to define a period and give it a special name, it's necessary to look at a few facts.
Early Latin — before the first century BC — is quite scarce. There are fragments of the early poets Naevius and Ennius, and the plays of Plautus and Terence which date from about 260-160 BC. There is a good deal from other sources but, taken all together, they don't really amount to a homogeneous, or even an identifiable style of Latin. In poetry, things look up with the De Rerum Natura of Lucretius, who lived from about 95-55 BC, but the best was still to be written, beginning in the middle part of the century by such as Cicero and Caesar, both great and acknowledged stylists. Catullus is the best-known poet of the period.
After that period literature blossoms with the advent of the whole clutch of writers whose style is conventionally called 'Classical' — Virgil, Livy, Horace, Propertius are among the more celebrated, flourishing around the beginning of the Principate of Augustus. You might decide that the Classical period began at roughly the time of Cicero's consulship in 63 BC, but others might prefer to choose a rather later date, when our sources come into full flow introducing the style known broadly as Golden Latin.
After the accession of Tiberius in AD 14, the flow begins to tail off, and there is, or used to be, a body of opinion that the end of the Classical Period should be conveniently taken to coincide with the end of the first principate. The peculiar, indeed alarming, years under the Julio-Claudians that followed have produced very little that is extant, though there are plenty of indications that writing remained in fashion, certainly of history.
After the turbulence of the 'Year of the Four Emperors' comes another surge, though it was prudent for writers to be cautious in expressing themselves. This applied less to the Elder Pliny and the histories of one kind or another such as those by Tacitus and Suetonius than to the more celebrated poets Martial and Juvenal. This is the age of Silver Latin, which was agreed by contemporaries to be of a lesser quality than that of a century earlier.
Others may argue for something differing from what I have suggested. To extend the Classical Period as far as AD 200 is, in my own opinion, a bit extreme; but if you really must define the Classical Period, you could do worse than pick out the reign of Augustus, and leave it at that.
