This effect can only be activated once during the End Phase of the turn this card was Special Summoned [sic]. (It cannot be activated again even if the activation or effect is negated.)
If your opponent controls "Genex Neutron" during the End Phase of the turn in which "Genex Neutron" was Normal Summoned, then your opponent can activate the effect.
If "Genex Neutron" is flipped face-down, such as with "Book of Moon", and then flipped face-up during the turn in which it was Normal Summoned, then you can still activate the effect of "Genex Neutron" during the End Phase.
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.