SA was hit with more than 423,000 lightning strikes, damaging winds and torrential rain on Saturday causing widespread damage, with 500 reports of wires down, and minor flooding.
By Monday, blackouts persisted in areas of the Eyre and York peninsulas, across the Adelaide Hills and suburbs and through the Riverland.
"SA Power Networks has mobilised all possible resources and has called in interstate field resources to assist," head of corporate affairs Paul Roberts said.
"Rebuilding and repairing the network and restoring power will continue into Tuesday and possibly beyond."
Mr Roberts said SA Power Networks understood long delays in restoring the grid were frustrating for customers but those still without power on Monday should plan for an extended outage.
The weekend storms also caused rocket manufacturing company ATSpace to abandon a launch from the Southern Launch Whalers Way complex on Eyre Peninsula.
The prolonged electrical activity caused damage to the electrical systems of the launch vehicle requiring repairs to be carried out off-site.
ATSpace chief executive Yen-Sen Chen said the launch of the Kestrel 1 rocket had been scrubbed until further notice.
"ATSpace will carry out thorough checks of the rocket system and we will resume the launch campaign as soon as possible," he said.
Southern Launch chief executive Lloyd Damp said the company had infrastructure in place to manage electrical storm activity but the volume of lightning strikes in the area was unprecedented.
With the clean-up continuing, police urged motorists across the state to take care with traffic lights in some areas impacted by ongoing blackouts.
Meanwhile in the north of the state, issues with phone services left a number of rural communities, including Booborowie, Burra, Copley, Gidgealpa, Hallett, Leigh Creek, Marree, Nepabunna and Yeelanna, unable to contact triple zero.
In the 2016 statewide blackout, storms damaged major transmission lines in the state's mid-north which tripped most of the SA power grid, blacking out about 850,000 properties.
