Zille was yet again embroiled in a Twitter debate with TV personality Sizwe Dhlomo over colonialism.
Zille cited positive aspects of colonialism during their debate.
On Wednesday, DA leader Mmusi Maimane’s spokesperson, Portia Adams, also said she was not in a position to respond on the matter.
Gottschalk said: “Any party will hesitate more in taking action against a former national leader, which could prove divisive among its members.
“Some of Zille’s previous tweets have received flak in a way her speeches, articles, and blogs never have.”
He said the party might insist her future tweets should go through their media office prior to publication, “to avoid future controversies”.
The debate started after Dhlomo tagged Zille in a tweet from “The King Centre” stating that there was “nothing righteous, just or positive” about the slave trade.
To which Zille responded: “I agree, there was absolutely nothing positive about slavery or the slave trade.
“If you read the transformed South African history textbook you will see the acknowledgement that, despite its many evils, colonialism helped end slavery in parts of Africa.”
She argued that “historical events can be inherently evil, but aspects of their legacy can turn out to be positive, although the positive does not cancel out the negative”.
This lead to Dhlomo to respond: “You, like it or not, are a beneficiary of colonialism albeit indirectly.
"Your biases, whether you’re aware of them or not, make it unlikely for you to be able to accurately weigh up the negatives of colonialism versus these positives you speak of.”
Commenting on Zille’s string of tweets on colonialism, Gottschalk said: “First, no one expects the Belgians, for example, to be grateful to Germany (for) any innovations they may have introduced during their World War I occupation of Belgium.
“Second, African countries which were not colonised, such as Ethiopia and Liberia, imported from abroad the same electricity generators, piped water, and airlines as those which were colonised. Under independence, they have all adopted the internet,” he said.
Zille on Wednesday spoke on Cape Talk radio where she defended herself and attacked the Cape Times for reporting on the incident and Independent Media chairman Dr Iqbal Survé.
Zille’s office had been approached for comment but did not respond.
Cape Times editor Aneez Salie said: “It has become a pattern for the premier to refuse to respond to our many and consistent calls for comment or clarity, yet she then later uses other media, where the Cape Times is not present, to rubbish our name and that of our executive chairman, where we cannot defend ourselves or indeed put questions to her.
“We feel this is the arrogant and cowardly behaviour we were used to under apartheid, and didn’t expect to encounter in a democratic South Africa.”
She later tweeted to the Cape Times: “You guys can really manufacture a ‘scandal’ over absolutely nothing.
"A guy starts a conversation with me, I answer rationally and reasonably, and you turn it into an outrage. Bizarre, especially when there is real news in the world out there.”
Last year, Zille faced a disciplinary hearing and was ultimately suspended by the DA after she tweeted about the “positive” aspects of colonialism.
Soon after the incident, Zille tweeted an apology. Earlier this year, Zille came under fire after she tweeted that colonialism brought the benefit of the water-piping system.
The DA then issued her with a letter cautioning her to stop tweeting about matters that did not concern the government of the Western Cape.