“Do this only once each turn” refers only to the ability it is attached to, not other instances of the same ability. In other words, if you control multiple copies of Riveteers Ascendancy, you will be able to do this once for each of them.

Once you have chosen to return a creature to the battlefield, further instances of sacrificing creatures the same turn will not cause the ability to trigger.

If multiple instances of the ability are on the stack, you will be able to return a creature to the battlefield for only one of those instances. Once you do that, other instances will do nothing as they resolve.

“Do this only once each turn” refers to returning a creature card from your graveyard to the battlefield using the triggered ability. As long as you haven't yet chosen to do that this turn, all instances of sacrificing a creature will cause Riveteers Ascendancy's ability to trigger.