It is generally recommended to store exosomes in a freezer (i.e., -80°C), if immediate viewing isn't possible, to help slow down dye degradation and preserve fluorescence for longer periods.
However, fluorescent dyes, especially those with shorter excited state lifetimes (which means it spends less time in its excited state before emitting light and returning to its ground state), can lose their fluorescence over time due to photobleaching or other degradation processes. Cell Brite 488, when compared to other dyes, tend to have a shorter excited state lifetime. So, it would be better to view exosome samples stained with Cell Brite 488 fluorescent dye as soon as possible to minimize degradation and decreased fluorescence over time. Cell Brite 488 can fade with prolonged storage, even at -80°C.