Eight large panes of glass were dislodged in a storm last weekend, with some falling on to the inner concourse of the Grade II-listed station.
The Tithebarn Street and the city centre-facing sides have been cordoned off by Lancashire County Council and will remain closed into the New Year.
Stands on the opposite side have now been closed after surveyors found problems with the window frames.
It is hoped the stands will reopen on Tuesday.
More stands at Preston bus station have been closed following gale-force winds.