We demonstrate a cryogenic buffer gas-cooled molecular beam source capable of producing bright, continuous beams of cold and slow free radicals via laser ablation over durations of up to 60 seconds. The source design uses a closed liquid helium reservoir as a large thermal mass to minimize heating and ensure reproducible beam properties during operation. Under typical conditions, the source produces beams of our test species SrF, containing 5 × 10 12 molecules per steradian per second in the X 2 Σ(v = 0, N = 1) state with a rotational temperature of 1.0(2) K and a forward velocity of 140 m/s. The beam properties are robust and unchanged for multiple cell geometries but depend critically on the helium buffer gas flow rate, which must be ≥ 10 standard cubic centimeters per minute to produce bright, continuous beams of molecules for an ablation repetition rate of 55 Hz.