Cost-saving measures by East Dunbartonshire Council (EDC) would see 24 of the authority area's 36 primaries closed or merged.
The move has prompted what the council called an unprecedented volume of FoI work but parents say they are increasingly frustrated by delays to their requests for information.
Wendy McLaren, a spokeswoman for the Save Bearsden Primary Campaign, said: "The council's repeated failure to provide us with information smacks of an organisation in disarray over ill-conceived proposals."
The campaign has been backed by a number of high-profile figures, including Children's Laureate Julia Donaldson.
A request for copies of emails and letters relating to the review has been denied on the grounds that "these views were provided in confidence without the expectation that they would be made public".
EDC has written to parents to say replies to further requests will not be given within the statutory 20 days due to staff sickness.
Mrs McLaren added: "We are calling on EDC to act in a transparent manner and to be honest about its planning processes."
Gordon Currie, East Dunbartonshire's education chief, said: "We continue to work through these requests and are making every effort to respond as close to deadline as is possible."