The US visa is sometimes invalidated. I wouldn't say this happens automatically. Sometimes it's invalidated and sometimes it isn't. If someone crosses the border from the US to Canada to claim asylum, any valid visa is generally invalidated by the US.
There is a detailed cessation thread in the Citizenship section of the forum that discusses this. Based on how IRCC is evaluating cases now, it appears that using your home country passport does not impact citizenship provided you don't return to your home country. If you return to your home country / country of persecution at any time before you have citizenshp, that's what causes problems and can result in PR status being revoked.
Thanks for the response. In our case we didn't cross the border from the US to Canada to claim asylum. And I'm perfectly fine to reapply for US visa.
3 quick follow-up questions:
1. is there a way to check whether my current US visa is still valid or not?
2. can I reapply for the US visa using my home country passport, or I absolutely can only apply that using RTD?
3. could you be so kind to share with me the IRCC article on "using your home country passport does not impact citizenship provided you don't return to your home country"?
The reason is that it's been almost a year since I applied for RTD and still no response on what used to be 20-day process. It might take another year or two or even longer to get the RTD, I just wanted to visit my grandson in the US, not going back to home country.
Many thanks!