The 19-year-old, who has netted winning goals against Droylsden and Workington during his first month at The Jakemans Stadium, will now remain with the Pilgrims until at least November 26.
The Chesterfield youngster, who signed a professional deal at the b2net Stadium in the summer, has made two starts and four substitute appearances during his initial month-long loan spell with United.
Burrow has also been granted permission to play for the Pilgrims in the FA Trophy.
United enter the competition at the third qualifying round stage on Saturday November 26 — with the draw anticipated on Monday November 7.