HF (3-30MHz) radios use ionospheric reflection to reach distances way beyond the line of sight. Radio waves in this segment typically "bounce" on a region of the atmosphere, back on the Earth's surface then back on the atmosphere a couple of times. If the conditions are right they can reach almost any area of the globe, independently of any infrastructure. This is why the military, the aeronautic industry, any sea-going ship and most critical emergency services have at least one HF radio as a backup. Back in WW II there were no satellites so HF propagation was the only way to communicate over long distances from a boat or an airplane.
The atmosphere has different layers and they have different properties when it comes to HF radio waves: some are transparent, some absorb, some reflect and these properties constantly change with the level of ionization, frequency, time of day and even weather patterns (mostly relevant to VHF and up). A low-medium level (this happens all the time to a certain degreee) of solar wind will ionize the F layer (the outermost layer that is relevant for radio propagation), which in turn becomes a "mirror" at HF frequencies and starts reflecting radio waves back to Earth. A medium-high level (typically during solar maximum) will result in very good ionization of the F layer and will also break through to the next next layer (E): this is what some of us hope for, as at this point F-layer reflection propagation mode is quite reliable on HF and you also get patches of ionized E layer that reflect VHF signals to really long distances. A high & very high level of solar ionizing radiation (like during a solar storm) will make its way down to the D layer, which is the atmoshperic layer that absorbs radio waves; this is what we don't want and sometimes it gets so bad that makes it in the mainstream news.
As for the geographic location, Guadalcanal is in the
Equatorial anomaly.
TL;DR: Solar Minimum = no HF propagation because the atmosphere isn't ionized so it doesn't reflect radio waves, Solar Storm (more frequent around Solar Maximum) = no HF propagation because ionization is so bad that radio waves are absorbed.
By the way, we are currently at the lowest Solar Minimum in modern history.