A pattern of resident firings is worrisome. Do they do a poor job of screening people they interview/rank (are they taking just #'s or are they factoring personality/fit)? Do they have unrealistic expectations? Are they malignant and foster an environment that makes residents miserable? Do they have any way to identify problems early and attempt to rectify them?
Multiple firings is a red flag, but how many is too many is impossible to answer. Too many factors related to the resident him/herself. Sometimes residents just suck, but they should be identified and assisted with transition to another training program rather than fired (unless they did something egregious, like lying).