Yes, they have the right to say whether you get the raise or not--there is no law guarantying you a cost of living raise, annual raise, or any other sort of raise; it is 100% voluntary on the part of the employer to give you a raise, and it being voluntary, they can put any requirements, rules, conditions, etc. on whether you get it. Remember: you don't ever have to get a raise: it would be legal for you to work 50 or 60 years without a raise. The employer chooses whether to give you a raise.