Nope! I never give up on a student, unless they are not willing to do the practice to progress. As long as the time and energy is spent between lessons, even singers that think they’re “hopeless” have improved with lessons. Sometimes habits of constriction can be present for years, this can and usually does take awhile to replace with habits of vocal freedom. I’m very precise in explaining what you need to move in order to feel more comfortable in the throat while singing, so usually it’s a matter of remembering what to do and what not to do and discovering the sensation of physical freedom every time you get the steps right.
Often I will suggest things that can help with constriction outside of lessons, such as the Alexander Technique, Somatics, and sometimes physical exercise that moves the lats, abdomen, hips, and back if the constriction is coming from too little energy in singing.
The only case in which I would stop lessons with a student based on inability to sing is if they literally have polyps, nodules tumors, or some other structural change in their throat that impedes their ability to make sound. In that case though, they should be going to a doctor not to me!
There is no minimum talent level required for someone to have lessons with me. That is an outdated approach to teaching voice lessons, and unfortunately most of the media today suggests that you first have to have some amount of talent before you can learn to sing. No. Completely wrong. If that were the case, I wouldn’t have students that have been so excited to do sounds they have never done before, and win competitions with those sounds!
If ever a voice teacher turns you down because you’re not “good enough”, you don’t want lessons with them anyway. Most likely, they have no idea what they are doing and are very insecure/embarrassed about this so they blame you. Often these are people who are not serious or passionate about teaching, and just need side cash. Not recommended!
I do believe there is a minimum energy and time level required to learn new things in your singing. Some people are willing to invest that, and others are not, those that do have a musical skill that lasts them a lifetime, and feel better throughout all of their speaking, singing, and breathing for the rest of their life.
So if you’d love to sing, but don’t like the sounds you make or how it feels when you sing, take voice lessons! You can only get better and change what you think is possible for yourself. 🙂