Origins
To persist is to keep standing when everything says fall. The word comes from Latin persistere — per- ('through, thoroughly') plus sistere ('to cause to stand, to stand firm'). The image is physical: a person braced against wind, standing through the storm.
Latin sistere is the causative form of stāre ('to stand'), and it produced one of the tidiest verb families in English. Each member combines sistere with a different preposition, and each preposition changes the direction of the standing.
Assist: to stand by someone. Consist: to stand together. Desist: to stand away, to stop. Exist: to stand forth, to emerge into being. Insist: to stand upon, to demand. Resist: to stand against. Subsist: to stand beneath, to survive on minimal support. Persist: to stand through, to endure.
Proto-Indo-European Roots
The broader root *steh₂- ('to stand') may be the most productive in all of Indo-European. From it English inherits stand, state, station, status, statue, stable, constant, instant, obstacle, substance, distance, circumstance, and dozens more.
Persist entered English in the 1530s, during a period of heavy Latin borrowing. The word filled a gap: English had endure from French and withstand from Germanic, but persist captured something neither quite expressed — the stubborn, deliberate choice to keep standing.