Hello. In addition to troubleshooting your problem here, I would also strongly encourage you to reach out to Asrock support. I own two of their boards (B350/B450) and I've found their support to be quite good. With that said, I have some questions for you:
"Shutting off": Could you be more specific? Is the PC power completely shutting off? No light or indication of power, such as fans spinning? Or is the display simply going black? Or is the system power cycling (rebooting) while gaming?
CPU: You currently have a Ryzen 7 5700X. Did you previously have a different AM4 CPU? If so, which one? Did these problems only start once you upgraded the CPU or some other component?
"CPU might be overheating?": I've personally never seen excess CPU temps shut down the computer, only reboot it. And with that being said, 71C isn't high enough to cause either condition. By the way, which CPU cooler did you employ?
RAM: Corsair CMW 32 gigs 3600 DDR4: What does CMW mean? "PC only runs them at 1066 ". 2133MT (1066 times double density rating speeds). When you attempted to set the speeds higher than default 2133, did you simply attempt to enable XMP or did you manual set the speed? Is XMP currently off or on?
Motherboard - Asrock b450m hdv r4.0: is 4 pin PCIe socket currently connected to power supply? I assume that it wouldn't boot otherwise, but I have to ask. I also question whether a 4-pin PCIe connector can supply enough PCIe slot power to a 3070 Ti, in addition to running the rest of the connected components.
GPU: What is the exact mfg. & model of 3070 Ti that you've used? Can you supply a link to the product page on amazon or newegg? This question relates to my question above about the motherboard only having a 4 pin PCIe connector, as opposed to an 8 pin.
PSU: You stated that you have a Corsair RMx 1000, which was three weeks old when you started this message thread. What event motivated you to purchase this new power supply? Was it purchased as a reaction to your PC shutting off? Also, what PSU did you have immediately before? (mfg & model?).
SSD: Did you originally install Windows on this AM4 platform, or was it initially installed on an Intel build, and the drive was simply moved over to this AMD build afterwards? I ask, because doing so can create incredible instability, including system reboots. However, I've never heard of it completely shutting off power.
Overclocking: Do you have PBO enabled or any other form of overclocking?
By the way, I apologize for my verbose response, but I'm just trying to help you figure out what's going on with your system.