The call comes as NHS Forth Valley updates its advice on visiting arrangements.
The health board said patients would continue to be able have at least one visitor at a time, and up to two people for essential visits.
These include supporting people with dementia, learning disabilities and autism.
There are no restrictions on time or the number of people providing support for patients receiving end of life care.
The board’s arrangements are aimed at keeping everyone safe, and will be kept under review as it works towards re-instating the way it operated before the pandemic.
Thanking families for their patience, Professor Angela Wallace, director of nursing, NHS Forth Valley, said: “We know how much patients benefit from seeing friends and family and these arrangements are designed to strike the balance between supporting visits while keeping patients and staff as safe as possible during the ongoing pandemic.
“We will keep these arrangements under review and hope to extend them further as soon as we can.”
NHS Forth Valley “strongly recommended” people to have a voluntary lateral flow test prior to visiting and then undertake these twice per week.
They must also wear a surgical face mask at all times during their visit rather than a fabric face mask or covering.
Supplies of single use blue disposable face masks are available at main hospital receptions.
Hand sanitiser must also be used before entering the hospital and before and after they leave,, and visitors must maintain physical distancing during their visit.
Women will be able to have one person accompany them to ante-natal appointments and maternity scans and up to two birth partners to provide support during labour and birth.
One birth partner and a designated visitor will also be able to visit after the birth.
Visitors are also asked not to bring additional family and friends with them unless they are a carer accompanying a visitor, a parent accompanying a child or visiting someone who is receiving end of life care.