Does a person lose his power after passing on One For All?
Yes.


   Im not sure how much of the Anime/Manga you have watched or read but its very clear that All Might is losing/has lost his power after giving it to Izuku Midoriya. 
 
 In the climatic battle against All for One in Season 3 its shown that the embers of One for All that All Might had left died out and he used the last of his power to defeat him.