In a care and protection DCF case permanent custody does not necessarily mean a termination of parental rights. Permanent custody and termination of parental rights are significantly different than permanent custody. If DCF has permanent custody you can seek to file something called a Review and Redetermination, where you have to produce some credible evidence that circumstances have changed since the child was found in need of care and protection and that DCF got permanent custody.
Once you are able to make that initial determination, then there can be a trial where DCF is still the one that has to prove clear and convincing evidence that the child is in need of care and protection. There are some technical requirements including, waiting at least 6 months and there is a process to do so, but even if DCF gets permanent custody so long there is no termination of parental rights, there are options to get custody back. Although, it might mean that you have to file a Review and Redetermination and have a hearing to have the Judge make that determination.