The age of onset of HSP varies tremendously, ranging from very early in life up to old age.
There are various mechanisms causing HSP, summarized
e.g. in Fig. 2 of S.Klebe, G.Stevanin and C.Depienne, Revue neurologique 171 (2015) 505.
There should probably be different reasons for different cases.
If some gene (protein) is wrong, one can imagine that trouble starts right at the beginning.
In a late onset case one could imagine that some kind of toxic substance ('Placques' in Alzheimer disease e.g.) accumulate over time and cannot be removed fast enough.
Does anyone have more concrete ideas about what is going on?