The most common confusion in maintenance contracts is this: the customer believes a resolution time has been committed to, while the contract commits to a response time. They are different things, and not knowing the difference turns into an argument in which, at the moment of a fault, both sides feel they are in the right.
Response time is the period between your notification arriving and the issue being logged and an engineer actually starting work on it. It is measurable, controllable and therefore something that can honestly be committed to. It should be written in hours in the contract, along with the channel (telephone, email, ticketing system) and the working hours covered.
Resolution time is the period until the problem is permanently fixed, and it is not under one party's control alone. If the fault lies in the software's own code, it is predictable; but if its source is a version change at your ERP supplier, an e-invoicing provider's service, the network infrastructure or hardware, or a corrupted data set, then committing up front to when the fix will be complete is technically impossible. Where a contract does commit to a firm resolution time, you should expect that commitment to be bounded by exception clauses; when reading the contract, assess the commitment sentence and the list of exceptions together.
An honest contract writes three things separately at this point: it commits to a response time in hours; for resolution it commits to a target time together with a workaround and a regular update interval; and it lists the dependencies outside its control openly. That leaves nothing to argue about when a fault occurs.
The second detail bound up with this is fault classification. The definitions of critical, high and normal should be written into the contract, and it should state who decides which class a fault falls into. A complete production stoppage and a single report adding up incorrectly should not fall into the same class; but nor should the supplier be expected to make that judgement alone in the middle of an incident.