As always with contract law, what does the contract say?
It is possible to have a time bar clause in a contract that limits or eliminates seeking damages if action is not taken within a specified time. Such clauses are commonplace in large contracts (e.g. construction and engineering, shipping, etc.) but may fall foul of consumer protection law in consumer contracts.
However, if the contract is silent, the law expects each party to be reasonably diligent in protecting their rights. In many, but by no means all, jurisdictions, there is an obligation of good faith on all parties in executing the contract - allowing a breach to continue so you can accumulate a damages claim smacks of not being in good faith. Even in jurisdictions with no obligation of good faith, there is an obligation not to act in bad faith.
Notwithstanding, you must mitigate damages so that any claim will be prejudiced to the extent that you contributed or failed to mitigate the damage.
In addition, with a breach that they know you know about, you open the door to arguments of waiver and estoppel:
Estoppel is a legal mechanism which prevents a party from departing from a promise or representation they have made to another party where to do so would cause that other party to suffer detriment. The concept embraces notions of fairness and reasonableness, as it is geared towards protecting a person who has relied upon an assumption or representation to either exist, or to come into existence. This is significant given that it provides an avenue for a party to seek relief outside the contract.
Estoppel can create new rights and be used as a cause of action in proceedings. It is also commonly used as a defence in the form of a ‘shield’.
Waiver by election involves the unilateral abandonment of a right or claim, and may occur where one party elects between two alternatives and inconsistent rights. Where one of those rights are satisfied, the other becomes no longer available for the party to assert. For waiver in this context to occur, there needs to be unequivocal words or conduct and knowledge of the right that is being waived.
Finally, we have statutes of limitations that preclude the bringing of any claim (without leave of the court) when a stutorially determined amount of time has passed since the cause of action arose.