Southern Railway is due to cancel all of its 2,242 weekday services on Friday after talks aimed at resolving a bitter dispute over driver-only trains collapsed.
Leaders of the train drivers' union Aslef met with the company for a second day at the conciliation service Acas on Thursday in an attempt to break the deadlocked row, but it ended without agreement.
Some 300,000 commuters are set to be affected by the third day of industrial action.
Passengers staged a protest at London's Victoria station on Thursday evening and handed in a letter to the Department for Transport demanding government action to end the crisis.
"We have suffered a year-long nightmare because of the collapse of Southern Rail. We have desperately called for government action and have been repeatedly ignored - even while many of us have lost our jobs, or had to move house," said a spokesman for the protest organisers, the Association of British Commuters.
Nick Brown, chief operating officer of Southern's owners Govia Thameslink Railway, said the company had put a "practical offer" on the table on Wednesday for the union to consider overnight with the aim of getting Friday's strike called off.
He said: "We're deeply disappointed, as our passengers will be, that Aslef has been unable to accept our proposals and we cannot find a way forward to end this dispute with the drivers' union at this stage.
"We're sincerely sorry that commuters' work and family lives are being punished with this unjustified and unprecedented industrial action. The unions must stop the pain and suffering blighting passengers and commerce.
"We will continue with our plans to modernise our railway and the services we offer customers. We urge the union to think again and work with us and move forward together."
Union sources said it was a "non-offer" which would continue the roll out of driver-only trains and did not address Aslef's concerns.
Transport Secretary Chris Grayling said: "I am deeply disappointed that this totally unnecessary strike action is to continue and causing thousands of passengers more disruption and misery. I have reaffirmed my offer for talks with the unions if they call off strike action, but they have failed to come to the table without pre-conditions."