Complex sentence: Republic's prominence which was brought on by the gold rush started to fade, prospectors and those who supported the mining industry moved away-during the years between 1900 and 1910--the town lost over half its population.
Split into simpler sentences: Republic's prominence, initially brought on by the gold rush, started to fade as prospectors and those who supported the mining industry moved away. During the years between 1900 and 1910, the town lost over half its population.