My sister refuses speech therapy?

Hi, so my sisters are twins and they're nine years old.

The last two years (I believe) they have been in speech therapy because they had serious trouble pronouncing their r's, l's, and occasionally s's. Mainly because it was hard for them to learn when they kept teaching each other to revert back to the bad speech (R's as w's and l's as y's).

I realize this is kind of a common problem for kids their age, but they weren't growing out of it. Anyway, last year at the end of third grade one of them (Let's call her twin 2) graduated from Speech. At this point, only twin 1 was left.

This year, we moved to a new town, and twin 1 demanded that she would not be put in speech. My mother, for some unknown reason, actually allowed this. Twin 1 says it's just "too embarrassing" to be pulled out of class.

This isn't some small lisp, she talks like she has since she was four, and she sounds half her age. She's supposed to be working on it but she never does.

This doesn't seem like something she is likely to grow out of, so my question is: Is it likely that she will grow out of it, or is it something that will stay the same or get worse? Thanks.