Is it customary to express heat loss as a negative number? In my chemistry class, we had a problem akin to the following:


  If an object with mass bla and specific heat bla is placed into a bla g calorimeter with an initial temperature of bla and a specific heat of bla, and the temperature of the calorimeter rises to bla at the end of the experiment, how much heat was lost by the object?


I performed the calculations and got an answer of, let's say, $8 J$. When I submitted this answer, I was told that it was wrong, and the correct answer would have been $-8 J$. Wouldn't this response to the above question mean that the object gained heat?
Your assumptions are correct, and from the wording of the question, the "correct" answer doesn't make sense, unless like you said, the object gained heat, which is possible; people have negative profits all the time. Sign conventions are not flawed in chemistry, but you just have to be careful when wording a question. To answer the title of your question, yes it is not only customary, it is necessary to express heat loss as a negative number, but the question still has to be phrased correctly--using the term "lost" serves as a negation in this use of language, the same way the unary operator in -1 serves as negation for a number. If heat loss were not expressed negatively, it wouldn't make sense because the system of an exothermic reaction must lose energy for its surroundings to gain it.