I got back on-site again today and finally fixed my problem! Well, not completely - but I certainly fixed it to my satisfaction. The details:
I ran a system restore (going back to a point made on 10/29, as the problem started on 10/30) yesterday in preparation for going on-site today. When I got to the house and plugged in the datalogger, I found that the system restore did no good. The device manager continued to show the same error with the Silicon Labs driver, and I wasn't able to connect to the station using WeatherLink.
I took the previous poster's advice and fully uninstalled all weather-related programs (WL, WxSolution, Cumulus, VirtualVP, N8VBvCOM, and the Silicon Labs driver) and restarted the computer. As an aside, I wonder why I didn't do this earlier - I guess I just expected the problem was something totally different. When I reinstalled WeatherLink, I found - to my delight - that it was able to communicate with the station! I checked the device manager, and, sure enough, there was no error shown with the Silicon Labs driver.
I next installed N8VBvCOM and VirtualVP. But when I tried connecting in VirtualVP (using the same COM port that WeatherLink had found the station on earlier), it didn't work. I checked the device manager, and the N8VBvCOM driver was flagged. I then tried to connect to the station again in WeatherLink, and it didn't work this time. I uninstalled N8VBvCOM and VirtualVP, then tried to connect to WeatherLink again. To my relief, I was able to connect to WeatherLink again, on the same COM port as before. The device manager showed no error.
So it appeared to me that the problem was with having N8VBvCOM and/or VirtualVP installed on the computer, since I was only able to communicate with the station in WeatherLink after they were uninstalled. I don't see how just having VirtualVP installed, not running, could cause a problem, so I suspected something was wrong with N8VBvCOM (considering the flagged driver in the device manager) or my configuration of it. But...
I had more software to test.
WxSolution was next. After uninstalling N8VBvCOM/VirtualVP and successfully testing the connection again in WL, I tried to connect in WxSolution - but it didn't work; WxSolution couldn't find the station on any of the given ports. I went ahead and installed a different version of WxSolution - one that uses a different method of communication with the logger (I don't know the details, only that the software designer changed the way it communicates in that updated version). With that version, I was able to detect the station in WxSolution - but was not, for some reason, able to connect to it live.
After failing to communicate properly in WxSolution, I tried Cumulus. I was thrilled to find that Cumulus was, indeed, able to communicate with the station! There were no problems - I simply selected the same COM port WeatherLink had found the station on and Cumulus connected to the station immediately.
So, I now have the laptop back on-site, running Cumulus 24/7. My previous configuration (9/30 - 10/30, before it went down) had VirtualVP, Cumulus, and WxSolution. WxSolution is the only loss in all of this. WeatherLink is on both laptops, but I only use the version on my main laptop and will continue to go down to the site every <53 days to download the contents of the datalogger onto it. That way, in case of a a power failure, laptop issue, or Cumulus issue that could prevent Cumulus from communicating directly with the station 24/7, I'll always have the 30-min WeatherLink data available. It's also nice to have the data on both laptops, in case I have an issue with either of them.
I'm very happy with the results of today, even if WxSolution and VirtualVP mysteriously don't want to communicate with my station. The combination of my 30-min WeatherLink logger data and more detailed 10-min Cumulus archive is perfect for my purposes.
If the remaining problem seems obvious to anyone, I'd appreciate hearing your feedback. If not, I hope those who contributed to this thread will see this post and know that the problem has largely been fixed. Thanks to all who have contributed!