My daughter also has selective mutism. She started talking to her teacher at the end of last year and this year we have also seen her improve slowly.
Her speech therapist has been extremely instrumental in helping her overcome her selective mutism. One of the things that I learned from her is that SM is primarily an anxiety based disorder.
Even when a child starts to overcome their SM, the anxiety doesn't magically disappear. The anxiety is still there, it perhaps is less severe or they are more comfortable in the environment. Nonetheless, it still can manifest in other ways.
Even though my daughter is talking at school, her anxiety does still show up in other ways, (being clingy to the teacher, needing extra reassurance, being worried she isn't doing the right thing, etc). She still is socially behind, because she lost out on a lot of social interaction while she wasn't talking at school. She's not as confident in her interpersonal relationships and is still shy with strangers.
Treatment for anxiety still needs to continue after the SM appears to be resolved.
In particular, the speech therapist has taught me to focus specifically on bravery.
- Reading books that encourage bravery: We read the book "I am brave" by Chelsea Gamache every night for months.
- Speaking positively about ourselves and our children and not be critical of them, to encourage positive self-talk and to not make a big deal about mistakes.
So to answer your question, while there may be a drastic change in some children where they seem to be able to talk quite quickly (something "clicks"), that is still not the end of their recovery, and time is needed for them to catch up socially, and work through the underlying anxiety.