The only three types of HPS lamps that I know that don't cycles, are the super high xenon pressure HPS lamps (They rarely cycles than regular HPS lamps at EOL), mercury free HPS lamps, and the unsaturated HPS lamps (Such as the Philips Ceramalux ALTO Non-Cycling,
Sylvania Ecoarc SPX 69/108W , Philips Ceramalux Retrolux, Iwasaki/EYE Sunlux Ultra Ace).
Regular HPS lamps usually cycles at EOL, but I know about the Chinese Osram NAV(SON)-E 150W and 250W, that
cycles only during run-up , than stabilizes and operates without cycling, until the next turning on. Operating these lamps continuously, may resulting in a non cycling HPS lamp, until they dims to orange SOX color and dies.