VA2-VA3 aren't as dramatic of changes. The main one that happens is they change to a smaller Power Supply that mounts to the bottom. I'd imagine that would help reduce assembly time as it's easier to assemble. It also reduces the complexity of the top case. The power supply itself is also smaller and less complex so I'd imagine that saved some costs too. Probably not huge savings, but still savings.
VA4 and VA5 is when it switches to the Model 2 case and we see the memory reset button, access LED, etc. dropped. I'd imagine the less fancy Model 2 case was where more of the savings came from here as it's a less complicated case in general to produce. At this point the Saturn hits the 20,000 Yen mark in Japan in March of 1996 and seems stays there for the rest of it's life in Japan. In the US it hits the $199 mark with these revisions. It doesn't drop in price again until June of 1997 when it goes down to $149 to match the PS1 that went down to that price a few months earlier.
VA6 is where the next major change happens and that's when we see the CD-ROM block consolidated down to 1 Chip. VA10 consolidates the SCSP, M68K and it's RAM down to 1 Chip, it's also where we start to see cheaper CD-ROM drives showing up. It should also be noted that these revisions all came out in 1996. So with the price holding at ~$200 from March of 1996 to June of 1997 I'd imagine the cost cutting from these revisions would have helped reduce losses.
VA15 is the last revision we see where the SH-2s are combined into 1 chip. This revision seems to hit around the later half of 1997. By this point the US price would be $149 for both the PS1 and Saturn but in Japan they'd still be at 20,000 Yen for Saturn and 19,800 Yen for PS1. Sony would drop to 18,000 at the end of 1997. From this point into early 1998 is about when Saturn production stops. Sony wouldn't drop their price again until the end of 1998 to $130 in the US, and about 15,000 Yen in Japan.
So while the price cuts in the first year and a half are aggressive from both Sony and Sega, you see it start to slowdown after the start of 1996. Yet behind the scenes they were still reducing the cost of the system. Around this time is when the Saturn starts to become profitable as they are able to reduce costs while maintaining the same price. The major issue here though is that Saturn was already failing outside of Japan and the Japanese market wasn't enough to keep things a float. This is why I think blaming it all on the cost isn't really the true issue. The real issue is the completely botched western launch that put them in a state they could never recover from.