Kinetic energy fluctuations of a non-dissipative 1D granular chain held between perfectly reflecting walls with various precompressions are numerically investigated. The dynamics of the system is explored for three cases, i) for a weakly precompressed chain which admits only solitary waves that break down into secondary waves under wall collisions, which is consistent with other findings in the literature; ii) for a strongly precompressed chain which exhibits mostly acoustic waves; and iii) for a chain with intermediate precompression. Case iii) accommodates a nearly stable solitary wave that travels unaffected through the acoustic waves and bounces back and forth between the walls for extremely long times. © Copyright EPLA, 2012.