A full investigation has been ordered after a Telstra hardware failure sparked the complete breakdown of South Australia's electronic monitoring system for 774 people on parole or home detention bail.

One alleged offender, on remand after being charged with attempted aggravated theft, remains at large after the 24-hour shutdown from early on Friday to about lunchtime on Saturday.

Premier Steven Marshall said the situation was unacceptable and that it cannot happen again. Credit:David Mariuz

It followed a similar but shorter shutdown in May of the system, which tracks people using electronic ankle bracelets.

"Cleary this is an unacceptable situation and clearly this is a situation that we cannot afford to occur again," Premier Steven Marshall told reporters on Sunday.