Stays ok...

"Holds out" in this context means to be okay or to work. For example: "I sprained my ankle recently. I hope my legs hold out tomorrow at the marathon." "My car is old. I hope it can hold out for at least another year."

"To hold out" is a phrasal verb meaning "to last" or "to persist," especially when faced with a difficult situation. Example: "The squadron was able to hold out under fire until reinforcements arrived." So in this context, it would mean that the speaker hopes they don't lose their voice before the end of their presentation even though they are having problems with it.

Doesn't stop working.