This is going to depend on the exact wording of the notification provision you hasd inserted in the contract. If that provision made notification essential to the contract. If that provision says that notification is essential, and that failure to notify voids the contract, then the other party knew that this was essential and if they broke this requirement, the contract is over. If it mere;y said that the client should notify the contractor whenever software XYZ is upgraded, that does not indicate that the notification is a condition of performance, or that failure to notify is a material breach, There are many ways that such a provision might be worded, withg different effects.
If the contractor is the one who drafted that provision, as the question implies, then any uncertainty would be resolved in favor of the client.
The contractor should also consider, what would s/he have done had the client given notice when the upgrade was done. Would that have changed things significantly? Or would the contractor have insisted on doing the upgrade or being involved?
Also, is such a provision reasonable? If an upgrade is needed ort strongly nadvised in the ordinary course of business, could the client reasonably be expected to notify the contractor when there was no current need for the contractor's services? Was the client expected to delay the upgrade pending the contractor's approval?
Also does the contractor really want to walk away from the contract, or really want an increased payment for extra trouble and work?
In any case, a useful answer is going to depend on the specifics of the contract, and of the entire situation. It may well also depend on the specifics of the local law, and the question does not indicate the relevant jurisdiction. This question is really beyond the scope of a forum such as this. The contractor will need to consult an actual lawyer, and provide that lawyer with details of the contract and the situation, to get useful advice.