Stories appear each year that announce new words which make it into the dictionary, but how do dictionaries decide what words to leave out?
There is indeed a process. Online dictionaries don't remove words, since a single entry takes up very little data and you might as well keep everything. That's what search engines are for, after all.
But printed dictionaries sometimes have to, because otherwise even the simplest editions, designed to help students or people learning to speak English as a second language, would get too cumbersome to use. Several categories exist before a word completely disappears, such as notations that it is historical (Now hist.), or even an obsolete (Obs.) term. If a word hasn't been used since about 1930, it gets labeled obsolete and is a prime target for reduction depending on the purpose and scope of a dictionary.
The cutoff is much earlier if the word is an obsolete or compound form of a current word, about 1800. So there goes our hope of never hearing about Donald Trump, Hillary Clinton or Bernie Sanders again. On the other hand, they provide solid job security for the word "carbuncle."