after you beat the Dragonborn main quest, before returning to Tamreil, all those "Illusions" appear that let you reset your Perks.

If I read the black book later, can I come back to this point and reset my perk later?

in a word yes.

it will always be that way just the same as the other books

You'll have to be on the island though. it doesn't work if you are in skyrim.

Yes, you can come back unlimited times. As said above, be sure to be on Solstheim as it is the only way it'll work.

Be sure to have a Dragon Soul when you want to reset your perks.