Longinus realizes that there's often a fine line in literature between what is innovative and sublime and what is contrived and affected. All too often writers, in aiming at the sublime, fall well short of the mark and end up producing work that, in its affectation, is frigid, lifeless, and utterly absurd.
A prime example of this lapse in taste comes in the course of a eulogy delivered by Longinus's friend Timaeus on the great Macedonian warrior-king, Alexander the Great. In attempting an elevated style of rhetoric, Timaeus unhappily compares Alexander to the famed rhetorician Isocrates, which Longinus finds singularly inappropriate. To compare the conquests of Alexander the Great to the panegyrics—public speeches of praise—of Isocrates is utterly absurd for Longinus but is nonetheless useful as a salutary lesson in the dangers of an overly-affected style.
Another example of frigidity is provided by the great Greek philosopher, Plato, someone whose written style Longinus usually regards as divine. However, in one particularly notorious case, Plato's normally sound judgement eluded him, when, striving for effect, he likened writing on tablets to the preservation of cypress memorials in the temples.
Such a ludicrously overblown comparison is frigid because it lacks resonance and cannot reasonably be applied to the living world as we know it. It is completely dead, frozen solid in Plato's text and unable to leap off the page to become incorporated into our everyday experience.
To be sure, Longinus doesn't think there's anything wrong with attempting an elevated style; far from it. It's just that he wants to alert his readers to the numerous pitfalls involved, the biggest one of which is a tendency towards absurdity and excess.