This can depend on the severity of the puncture, and the terrain on which you’re driving. However, thanks to technological improvements, tire plugs can last for a long time.
A tire repaired by a plug can drive up to 25,000 additional miles without problems, but do remember to check it for punctures and bulges regularly, as all tires should be checked.
If in doubt, have a trusted professional check your tire. They’ll be able to let you know whether you can continue to drive on the plug, or need to replace the whole tire.