Leaving aside the question about whether the dramatic population declines of First Nation people in North America could be called a "genocide", that population decline has not been (and is not now) "perpetual".

For about 400 years after the Colombian exchange began, Native American populations continued to decline. Recurring epidemic diseases were the main reason. In the United States and Canada population declined to a low point in circa 1900, after which inoculations and vaccinations began to counter epidemic diseases and many American Indian populations began to finally rebound.

Populations in both Canada and the USA have grown more than ten times since 1900.

First Nation populations further south in North America (Mexico and Central America) seem to have stabilized and begun to rebound earlier. This may be due to some of the diseases which were epidemic in the sparse Native American populations of the USA and Canada becoming endemic in the denser populations further south.

Endemic diseases are deadly, but less disastrous for population levels, as they tend to kill off children, while the adult population consists of the immune survivors.

In any event, populations of First Nations people have been growing strongly for over a century, so the decline has not been "perpetual".

Just a reminder that while discussion of First Nations issues through 1995 is fine (and I believe such a constraint doesn't limit overall discussion of this topic), we would ask that people respect the 20 year rule here, so if you want to talk about very current issues, we would ask you take it to another subreddit.