Thor lost his ability to become Donald Blake in Thor, Vol. 1, #337 (November 1983) when the magical ability was transferred by Odin to Beta Ray Bill and placed within his weapon, Stormbreaker. Thor returned to time-sharing a body with Donald Blake, as a fail-safe contingency after the Ragnarok saga and the death of Odin.
History:
If you are reading about Thor during his early time as Donald Blake, you are reading about the character who was created and first appeared in Journey into Mystery #88 first seen in 1966. This character would remain pretty much the same except for cosmetic changes for the next forty years.

Thor's father Odin decided his son needed to be taught humility and consequently placed Thor (without memories of godhood) into the body and memories of an existing, partially disabled human medical student, Donald Blake. After becoming a doctor and on vacation in Norway, Blake witnessed the arrival of an alien scouting party. Blake fled into a cave after they heard him and began to pursue him. After discovering Thor's disguised hammer Mjolnir, and striking it against a rock, he transformed into the thunder god.
Thor shared his physical identity with the handicapped mortal form of Donald Blake.
Mjolnir was hidden in the form of a staff used by the mortal Blake and when he wanted to become Thor, he tapped the hammer on the ground and was transformed.
In the beginning, if Thor was disconnected from Mjolnir for more than 60 seconds he would revert back into Blake. It happened more often than you would think. It was his only real weakness.
Mjolnir was far more powerful than Thor himself, often acquiring powers needed to defeat the villain of the day, and then that power was rarely, if ever seen again. A few powers were taken by Odin over the years, one of them being the power to travel through time.
Thor and his mortal form of Donald Blake would remain connected until Odin gives the power to Beta Ray Bill in Thor #337 (November 1983). Thor would operate with a secret identity as a construction worker named Sigurd Jarlson; a very big construction worker who wore glasses.

Sigurd Jarlson, secret identity of Thor, for a time.
Thor also spent time as the construct of Jake Olson, a paramedic who had been killed and replaced by the being known as Marnot (later revealed to be a Raven of Odin) in Thor Vol. 2, #1 (July 1998).
The being/construct Donald Blake was consigned to a mystical void until the death of Odin and the beginning of what appeared to be Ragnarok, the Twilight of the Norse Gods.
Upon Odin's death, Thor and Blake are reunited in that void and Thor is convinced to return to the world, once again time-sharing a body with Donald Blake, who apparently was a failsafe mechanism set up by Odin in the event of his death and Ragnarok.
Eventually this new Thor dies as well and replaced by a being named Tanarus, claiming to be a new thunder god.
Tanarus is Ulik, an enemy of Thor in disguise. Thor returns from the Realm of Dead Gods with the help of the Silver Surfer and Loki to defeat him.
- A curious note: After Thor's death at the hands of the Serpent, Blake and Thor become two separate beings again. Blake discovers his life was magically erased from the timeline. There was no trace of his existence. He still retains his memory of the events and skills from his time as a doctor. I suspect with the help of SHIELD he will find a new life in the Magical Beings Displaced by Time Protection Program.