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1. see you until next time

Does #1 make sense?

2. I saw her until she visited regularly.

I think 'until' is not with future meaning.
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No, #1 and #2 are not possible, but future has nothing to do with it. 'Until' requires a continuous event (or negative event) preceding a time point:

I will not see you until next week.

I saw her until she stopped visiting regularly.
Comments  
Students: We have free audio pronunciation exercises.
Wow... I just heard this from the BBC news.

1. Thank you for listening, see you until the next time.

So, until the next time in this sentence is OK but not in my example, isn't it?
1. Thank you for listening, see you until the next time. -- This is certainly not OK; in fact, it makes no sense. It is either a slip of his tongue or a slip of your ear.