Never give up on a life. And plants are alive.
I have 4 sick plants at the moment. (My collection is over 30).
The achievement that I am personally most proud of (with regards to orchids), would be rescuing one of my Vanda Blue Magic plants from the brink of death (it had one root left). Now, it has recovered (over a year later), with three long roots (look like tap roots), and nice light green foliage.
My sick plants are two Phalaenopsis (crown rot - I hate this disease, with one of the Phals it literally happened over night - and I have linked it to spraying too late in the evening), one poorly Paph. henryanum, and Vanda Exotic Purple which has lost almost all of its' roots...
I have a log book so I write down everything that I am doing. So as not to repeat the same cultural mistakes in the future.