“This is an undecided matter at the moment.
Note that the ability is acquired in layer 1, as part of the copy effect (so that other objects copying this one would also have the ability), not in layer 6.
Logically, then, the ability should be lost in layer 4 when the land's type is changed, however 305.7 says…
305.7 . If an effect sets a land’s subtype to one or more of the basic land types, the land no longer has its old land type. It loses all abilities generated from its rules text and its old land types, and it gains the appropriate mana ability for each new basic land type. (…)
where the “from its rules text” would exclude the ability gained in layer 1. This is contrary to the general philosophy of layers, where effects in each layer override effects in previous layers.
So the current answer is “it has the ability” but the answer should probably be “it doesn't have it.”
Daniel Kitachewsky
L3, Paris, France
Rules NetRep”
http://apps.magicjudges.org/forum/topic/3508/So, if you have Thespian's Stage which is a Mountain from Blood Moon with it's only ability it gained from copying itself, and then you use it's ability to copy another land (lets say, it copied a Hallowed Fountain), and then Blood Moon is removed from the battlefield, the Thespian's Stage will be a mountain with the thespian's stage's ability, or a Hallowed fountain with the stage's ability?