My sister is none the better despite our caring efforts.
Although we tried hard to cure her illnesss, my sister is none the better for it.
These two examples are a bit more natural sounding. The reason for this is that 'none the better' is a kind of describing or adjectival modifiying clause used in this case to describe the person's sister. So it has to follow the noun (sister), and the 'hasn't gotten better' cannot be used with a noun clause and must be discarded. 'It' refers to whatever action was taken that has not affected the subject, in this case your caring efforts or attempts to cure the illness.
Some other examples:
We studied all night but we're none the better for it.
I washed those jeans 5 times but it appears that they're none the better for it.
So again, despite studying, their situation has not improved. The stain in the jeans was not removed even though they were washed 5 times. Both subjects (jeans and we) are none the better for it, with 'it' being their respective situations (studying and washing).
This 'none the better' phrase is somewhat outdated, I don't think its widely used in modern English, it's something that's found more in literature if anywhere. Some older generation people may use it but in modern English the phrase "I'm no better off" pops into mind, or else the speaker may just revert to describing the situation directly.
I washed these jeans 5 times but they're still dirty.
We studied all night but we still failed the test.