Love, like fire, must be constantly in motion; it dies when it ceases to have hopes or fears.

[L’amour, aussi bien que le feu, ne peut subsister sans un mouvement continuel, et il cesse de vivre dès qu’il cesse d’espérer ou de craindre.]

François VI, duc de La Rochefoucauld (1613–1680) French epigrammatist, memoirist, noble

Réflexions ou sentences et maximes morales [Reflections; or Sentences and Moral Maxims], ¶75 (1665-1678) [tr. Stevens (1939)]
    (Source)

This maxim appeared in the 1st (1665) edition.

(Source (French)). Other translations:

Love can no more continue without a constant Motion, than Fire can; and when once you take Hope and Fear away, you take from it its very Life and Being.
[tr. Stanhope (1694), ¶76]

Love, like fire, cannot subsist without constant motion; it ceases to exist, as soon as it ceases to hope or fear.
[pub. Donaldson (1783), ¶273; ed. Lepoittevin-Lacroix (1797), ¶73]

Love, like fire, subsists by continual motion: when it ceases to hope or fear, it ceases to exist.
[ed. Carvill (1835), ¶234]

Love, like fire, cannot subsist without continual movement; as soon as it ceases to hope and fear, it ceases to exist.
[ed. Gowens (1851), ¶76]

Neither love nor fire can subsist without perpetual motion; both cease to live so soon as they cease to hope, or to fear.
[tr. Bund/Friswell (1871), ¶75]

Love is like a flame; it can never be still, and dies when it ceases to hope or to fear.
[tr. Heard (1917), ¶75]

Love, like fire, needs constant motion; when it ceases to hope, or to fear, love dies.
[tr. FitzGibbon (1957), ¶75]

Love, like fire, must constantly leap and dart; when it can neither hope nor fear, it dies.
[tr. Kronenberger (1959), ¶75]

Love, like fire, cannot survive without continual movement, and it ceases to live as soon as it ceases to hope or fear.
[tr. Tancock (1959), ¶75]

Love as well as fire cannot subsist without continual motion; and it stops living from the moment it ceases either to hope or fear.
[tr. Whichello (2016) ¶75]