a data point - too little to spend resources during data preparation?
Practically everything related to statistics (including Machine Learning) has to do with studying chance, i.e. trying to determine to what extent an observation is due to chance or not. 

For example one might want to know whether a drug actually helps with a particular disease or not. If we observe that one patient improves after taking the drug, there's not enough evidence to conclude since many other factors could have caused the improvement. This is why one needs a very strict protocol in order to obtain a statistically meaningful observation (two groups of patients, placebo etc.).
A reasonably high number of observations is needed, otherwise it's impossible to distinguish the effect of "chance" (any other factor) and the real effect of the drug.


  a) Is there any systematic/mathematical/theoretical approach that can tell me anything less than N% is too little to impact/influence the output?


The standard method for knowing whether an observation is due to chance or not is to use the appropriate statistical significance test. There are many of them and they depend on what exactly is being tested. 


  b) How do you decide which items are too little to impact output. Do you go with your judgement which is a subjective approach?


In ML it's common to take a more experimental approach, for example trying with/without an observation or feature and then evaluate which versions works better. Of course it helps to have an intuition of what is more likely to work. In general including extremely rare observations is a bad idea because it's likely to cause overfit, i.e. when the model "learns" something which is actually due to chance.



[added following OP's update]

In this case this is a resource allocation problem, I don't think  statistical significance is relevant here. Assuming that you want to optimize the use of manual labor based on how often a drug is used, i.e. the only thing to maximize is the sum of the frequencies of the drugs being labelled, then it's simple: rank all the drugs by their frequency in descending order, then proceed with manual annotation following this order. This way you're sure that the drugs which account for more patients are done first, so whenever manual annotation stops the largest possible amount has been labelled.