Can I steal a permanent indefinitely with Frenzied Fugue?
The "until end of turn" effect lasts until the end of the turn, regardless of whether or not Frenzied Fugue remains on the battlefield. 


  611.2a A continuous effect generated by the resolution of a spell or ability lasts as long as stated by the spell or ability creating it (such as “until end of turn”). If no duration is stated, it lasts until the end of the game.


If the effect read "[...] until end of turn or until Frenzied Fugue leaves the battlefield.", then you would lose control as soon as Frenzied Fugue left the battlefield.