Some accounts state this bridge was destroyed by fire in 1921. A brief mention in the July 18, 1926 edition of The Fresno Bee implies it was destroyed in June of 1926.
Catalog Number 1983/001/SBPM01034 - Sacramento Bee. This "Center for Sacramento History" catalog entry suggests the bridge survived until 1936. Given the bridge was ultimately replaced in 1940, this later date makes more sense than some of the earlier claims of it being destroyed in the 1920s unless there were some intermediate reconstructions.
Klamath River at Orleans - California State Library. This image shows a bridge of similar construction but apparently shorter span than the other images linked here. However, matching buildings seen in the background of multiple images place it at the same location. Given the muddled suspension bridge chronology at this location and frequency of Klamath River floods, it seems likely there were multiple reconstructions of this bridge.