GM is considering cutting 1,000 jobs at the Cheshire factory.
Unions were negotiating with management, but talks ended yesterday without resolution. Talks will resume next week.
GM said it wants to improve efficiency at the site, but no decision has been reached about its future.
The staff walked out yesterday following comments from Carl Peter Forster, GM European president. He said the only way forward at Ellesmere Port was to cut one shift from the plant, according to the unions.
GM Europe has said it is determined to handle the situation ‘as socially responsibly as possible’.
"For the future, it is important for Ellesmere Port that everyone works together to meet the continuing demand for the Astra," it added in a statement.
"We look forward to working together to give the plant the best opportunity to compete in the automotive industry in the long term."