Booking Upper Class Flights

I will be travelling to St Lucia in mid June. Friends advised me to book late as I may get a cheaper fare. But how late is too late?
Is there a best day or time to get best fare. I am totally clueless as to best thing to do as the fares seem very stable every time I look on the Virgin Atlantic site.
I would appreciate any advice
Anniel
Is there a best day or time to get best fare. I am totally clueless as to best thing to do as the fares seem very stable every time I look on the Virgin Atlantic site.
I would appreciate any advice
Anniel