Why would a reflector of an hps streetlight make it cycle?

I know one cause has to do with the amount of heat reflected back towards the arctube. Take Coopers for example, Too much of the energy is redirected back towards the lamp which can cause early lamp failure.

I've been told some acorns with "house side reflector" to direct the light to the roads and none to the house having 150 watt HPS tend to have early cycling too

Regular sodium vapor has the sodium vapor pressure regulated by the temperature of their cold-spot (where the amalgam capsule reside) so, the pressure is exactly the saturated vapor pressure on this amalgam.
And arc voltage drop increases with the pressure.
And if you redirect the radiation (mostly heat, but visible is important too) back to the arctube, it temperature will rise, so the arc voltage and when the ballast is not able to settle corresponding stable operating point, the lamp overheat, so the OCV would not be enough to maintain the arc, so it extinguish, so the lamp would cycle.
Rearranging reflections inside the luminaire is the best you could do, however if this is really not possible, use or special unsaturated vapor lamp type (intended for CWA), or an electronic regulated wattage ballast (most low frequency square wave types). It regulate the current so, the actual lamp watts are kept constant regardless of lamp voltage drop. This ensures, then the power delivered to the lamp would not rise with the lamp voltage, what is usually he case for magnetic. Beside of this the polarity change is nearly instant, so the lamp does not exhibit the reignition peak, as on magnetic, so it would start to cycle much later in the life (as the reignition peak is the point, after current zero crossing on the 50/60Hz lamp current waveform, where the lamp voltage is closest to ballast OCV)