Stata drops variables that "predicts failure perfeclty" even though the correlation between the variables isn't 1 or -1?

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I am running a logit regression on some data. My dependent variable is binary as are all but one of my independent variables.
When I run my regression, stata drops many of my independent variables and gives the error:

"variable name" != 0 predicts failure perfectly
"variable name" dropped and "a number" obs not used

I know for a fact that some of the variables dropped don't predict failure perfectly. In other words, the dependent variables can take on the value 1 for either the value 1 or 0 of the independent variable.

Why is this happening and how can I resolve it?

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