In 'Thor' he seems to have died,
Then , due to some sort of Asgardian force he is brought back to life and regains his powers.
So the Question is,
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As even his mother can die and his father (the former shown in Thor 2 and the later implied a few times that it IS possible during both films), one can clearly say that yes: Thor CAN die (through age and through force). Although it is very hard to kill him (even more so seemingly than the average Asgardian).