Paul, perhaps someone else or from Adobe have more (or otherwise) to say, but let me offer this: be sure to read the brief documentation on activation at https://helpx.adobe.com/coldfusion/using/coldfusion-licensing-activation.html
It indicates that with a normal cf license, there's no need to be online once activated. (So your getting the message you saw would seem odd.)
But note that it has a concluding section in "Activation of Virtual core licenses", a DIFFERENT kind of cf licensing which changes things: that MUST be activated constantly, or after a grace period of a couple of weeks it will revert to the free developer edition (limited to a max of only a couple concurrent ips at one time).
Note it also discusses how you can set up to get an email when that situation and grace period is happening. It's also tracked in the ui and logs.