Question

an atom retain the properties of an element, but why can't protons , neutron, or electrons retain it?

Answer 1

first of all a proton is a hydrogen ion. by definition elemental properties are not of ionic state.still it deserves thus a special status
chemistry is about interactions. let us check the whole gamut (i may be missing. chem is not my thing) of interactions we have: covalent, ionic, polar non ionic and van-der-vaals. let us put van der vaals in the side for the moment. the rest are to some extent about + and -. we have established that a proton by itself merits some recognition of an ionic state of an element.
neutron wont do - no +-.
an electron in the sense of chemistry exists somewhere in an orbital, without some "positive attraction" - no orbital - no mutual sharing of an electron (to whatever extent by the specific bond).
if we get back to van der vaals - this interaction (i think) is defined by the mere fact it does not partake in the "attraction game" it is in my eyes somewhat definition by exclusion. the aggregation is of molecules/regions that stay out.

one last thing: the protons set the number of free electrons (last orbital), and the ability of the nucleus to attract more electrons. once again from this definition it stands that electrons by themselves wont do too much, neutrons wont, and single protons are allowed in the "game"
i hope i am understood and that i am correct

Answer 2

protons aare + and electrons _ neutrons are nutreal ie+- all are present in atom