It's best to force update the license by deleting it and reactivating the same license key again because it may take time to have it updated automatically.
This depends on how SPLMS synchronizes license with the license server. This happens approximately every 2-3 hours. But in fact it depends on frequency of using SPLMS - the more users use SPLMS, the faster license will be synchronized with the license server. Each time a request from SPLMS is sent to the customer’s server a random integer value from 0 to 10 is generated. When it equals 0 the code for sending request to the license server works, otherwise it’s not sent. It basically means the more frequently SPLMS is used at the customer’s side the more is the probability the license request will be sent to the licensing server.
For the same matter it's important to use different keys at QA and production environments to avoid a license error. When reactivation request is sent from several servers for one key it will be counted as valid on one of them only eventually.
This is relevant in case QA server is not connected to the Internet as well. Once the license has been activated it sends reactivation requests every now and then. In this case when it sends reactivation request from production it will not find information of the previous activation and may fail.