Panchronic comes from the Greek words pan- and Chronos (time).
A panchronic approach to, say, language is an approach that includes every aspect or all dimension of time.
It must be understood in relation to diachronic and synchronic.
The diachronic approach focuses on the successive changes in language that have taken place over time, while the synchronic one explores language as a unified system of existing relationships. Thus the diachronic deals with time as a series of changes, and the synchronic deals with what happens simultaneously, without recurrences. Language must be studied in the light of its past (for example, the present form of the word in the light of earlier forms) or its present.
The panchronic approach would try to include both synchronic and diachronic.
Ferdinand de Saussure objected to the adoption of a panchronic approach and insisted that the study of language (langue), as opposed to speech (parole), could only take place synchronically.
In opposition to the neogrammarians (an influential 19th-century linguistic school that insisted that the only approach to language learning was historical), Saussure argued that the formal object of linguistics was language as a system fully realized and available at all times. In other words, he defended the synchronic study of language, not the diachronic study of language as something accomplished in the present, not as something evolving (that is, different today from what it was before).