I've used an ASUS XG Station Pro eGPU with an RX 580 and an RX Vega 56 as well as a Razor Core X eGPU with the RX Vega 56. I have only experienced three crashes where the eGPU either turned itself off or took down the whole system (all with the ASUS and the Vega 56). Once was when playing Star Trek Online and the other two were when running GFX Metal tests. The consensus was the Vega 56 was drawing too much power for the 330W power supply to handle, thus why I now have the Razor Core X.
There was a few people having similar issues you are experiencing with their eGPUs a couple of years ago (I will post the thread if I can find it) and it was determined that it was the quality of the provided Thunderbolt 3 cable. A majority of them (including myself for good measure) replaced that cable with Apple's TB3 cable and it resolved their issues.
The manufacturer of the video card has been found to cause issues as well. Sapphire is the most reliable (from what I've seen), but after that your results can swing wildly from good to awful. What brand of card(s) are you using?
I assume you are using the MBP's screen (ie no external monitor) which requires the signal to go from the MBP to the eGPU and then back again, which is twice the throughput I need, since my signal goes from my mini to the eGPU to my monitor. That means you want a good quality cable (see above).
Also, what macOS version are you using? Mojave's support for eGPUs was okay (mostly livable), Catalina's was better (depending on your needs), but Big Sur (at least for me) has been really good (and much better than both Mojave and Catalina, but YMMV).