Polar connotations in the same word: 断り and 惜しい


Recently I bumped into two words「断り」and「惜しい」.

  * Accordingly to Jisho:「断り」can mean permission; consent​ but it also can mean rejection; refusal; nonacceptance; declination; declining​... 
  * As for「惜しい」 it can mean regrettable; disappointing; unfortunate​ or also precious; dear; valuable​... 

Of course, in the case of 「惜しい」 these meanings are not exact opposite but
still one conveys a positive connotation and the other a negative. I'm aware
that any language has some words with polar meanings.

> My question is, besides context, in Japanese is there a rule of thumb that
> one could use to identify if the connotation is positive or negative?

