A ballot of Unite union members at Defence Support Group (DSG) has been extended until Thursday of next week.
Bosses have offered a £1,250 lump sum after a series of strikes over pay last year.
DSG repairs and maintains military equipment for the Ministry of Defence (MoD).
Its land division is set to be sold to new private bosses Babcock on 1 April.
Brett Davis, Unite convenor at DSG Donnington, told Socialist Worker he had been arguing to reject the deal.
“Make no mistake, there’s an offer on the table that wouldn’t be there if we hadn’t taken action. It shows action can win,” he said.
“If we reject there will be no going back—we’ll have to fight to win.
“That means everyone on the picket line, getting coachloads of us down to the MoD and Babcock to protest.”
Fighting back has made workers stronger.
Unite’s initial industrial action ballot went out to just under 800 workers. The ballot on the offer goes to around 1,000.
The Prospect union has accepted the new offer, but the PCS union remains in dispute and could join further strikes.