Caitlyn, seven, and Harley*, two, were taken into foster care after their biological parents were unable to provide the level of care they needed.
But now Blackpool social services are struggling to find a home for them due to a shortage of carers willing to take on two disabled children.
Victoria Gent, chairman of Adoption Lancashire and Blackpool, said: "Brother and sister groups are among the children who wait longest to be adopted, as there are simply not enough people coming forward who are able to give them what they need.
"Caitlyn and Harley share a close sibling bond so it is absolutely vital that they are kept together.
"They are desperately searching for a loving family that can provide the love, warmth, and support that they need.
"Unfortunately, this is proving difficult, which is why we are making this appeal to the people of Lancashire. If you think you can help these children, please get in touch."
The signs and symptoms of Caitlyn and Harley’s condition can vary widely and due to their young age, it is not yet clear how their disabilities will affect them as they grow and develop, Lancashire County Council said.
An event for potential adoptive parents for the pair has been arranged for 6pm on Tuesday, May 10, at the County Hall in Preston. People who are interested in attending are asked to book a place online.
Caitlyn and Harley
A Lancashire County Council spokesman said: "Like most children her age, Caitlyn enjoys being outside playing games, and loves playing hide and seek with her little brother.
“Caitlyn's confidence at school is growing, she receives extra support from her teachers and they set schoolwork that is tailored for her as she needs work set that is for her learning age, which is about two years behind some of her friends. Caitlyn also requires lots of emotional support to help her manage her feelings and her friendships.
“Little Harley is a busy, happy and laid back little boy. He is sociable, inquisitive and is starting to say a few words. Harley goes to nursery and playgroups each week, which is helping to develop his speech and social skills. His foster carers also help him learn at home through play and reading.
“Harley enjoys watching the bin lorries coming to empty the bins each week and even has a collection of bin lorry toys which he loves playing with.
“While there is lots of support already in place for Caitlyn and Harley and their carers, further support is available to help both the children and their new family throughout their adoption journey. Adoption Lancashire and Blackpool have a designated Adoption Support Team to help the adopters at every stage.”
*Children’s names have been changed to protect their identities