Following a delayed start 34 overs were bowled, in which Gloucestershire moved on from 31-0 overnight to 120-1.
After a long delay, the two teams came back out under the lights at 21:00 BST, but the visitors remained untroubled.
After 21 from Chris Dent, Bancroft got to 69 with Will Tavare still there on 43 as the visitors closed on 150-1.
Having begun the day with fears of following on, on his 50th first-class appearance, Tavare's unbroken stand of 88 with Australian Bancroft, who passed his previous season's best of 53, leaves Gloucestershire just 59 runs short of that initial target.
But against a Sussex side who are unbeaten in seven matches with Gloucestershire, there is little hope of the visitors improving on their record of just two wins from 18 visits to Hove.

Cheick Cisse, who won taekwondo gold, was given $85,000 (??64,000) and Ruth Gbagbi, who won bronze in the women's event, got $51,000.
Cisse's gold medal was the first in the country's history.
Last year, President Alassane Ouattara made similar awards to members of the national football team after they won the African Cup of Nations.
He did not reveal any details about the houses given to Cisse and Gbagbi, or their location.
More on this and other African stories
Mr Ouattara and his wife Dominique wore the medals as they posed with the athletes for photos at the presidential palace in the country's commercial capital, Abidjan.
Ivory Coast had only won one Olympic medal until this year.
Gabriel  Tiacoh won a silver medal in the men's 400m in the 1984 Olympics in Los Angeles.
He died in 1992.
Ivory Coast used to be one of Africa's richest countries but its economy has been devastated by years of conflict.
Cameron Bancroft made only his second County Championship half-century of the season as Gloucestershire reached 150-1 against Sussex at rain-hit Hove.
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Ivory Coast's two medallists from the Rio Olympic games have been given cash awards and houses by the president.