According to Official Guinness Records,
The most holes of miniature golf played by a fourball in 24 hours is 1,440 and was set by two teams from MGC Olympia Kiel e.V. at Miniaturegolfhalle, Rendsburg, Germany from 19-20 March 2005
Team A: Marco Balzer, Daniel Christ, Leif Markmann and Jan-Christophe Theden Team B: Hans-Knut Martin, Rene Lemke, Ralph Brandt and Thilo Thomsen They did 80 complete rounds of 18 holes as a fourball 18x80=1440. As the name suggests this was an indoor course.
For a complete list of 2005 records, please visit 2005 Guinness Records in Germany.