The 33-year-old will now be with the Iron until the away game at Colchester on Saturday, January 12.
Mildenhall has made five appearances since signing for United at the start of November.
Manager Brian Laws told the club's official website: "I'm delighted with that because we feel that the experience, knowledge and ability he possesses is of great benefit to us.
"He has also gelled really well with the players and they've responded to him."
- Sports & Recreation