Can dysautonomia progress over time?

Depends what it is. From. For example, dysautonomia from a traumatic brain injury, once stabilized and out of early storming, will remain fairly stable. If it is from a progressive disease like ms, it can get worse. Dysautonomia can also be aggravated by certain things, such as infections, that can make it feel like it is progressing. A thorough history would be needed to suggest whether it is suggestive in each case.