Yes, the AcuSpike Spike Trainer can be left outside. While the Acuspike was designed for indoor use, the majority of parts are durable and will withstand outdoor conditions.
The base of the machine and its parts are resistant to the elements. All exposed painted surfaces are covered with industrial grade powder coat that contains UV inhibitors, which is the standard for all high quality outdoor equipment. The hand crank has a marine grade zinc coating that is made to be exposed to the elements.
The AcuSpike Spike Trainer will last longer against the elements if you follow these recommended steps. For best longevity, the rail assembly should be stored indoors and the top of the post should be covered to prevent water from entering (a plastic container would work well). Minimally, you should take off the rail assembly, cover the post and remove the hopper and foam ball grips (which are not UV inhibited and will degrade if exposed to long periods of direct sunlight) to be stored indoors. If the AcuSpike is left outside and unused for a prolonged period of time, covering the entire base will help to preserve it's appearance from degrading due to the build up of dirt.