This current version of Logos (49.0.144) cannot open or close without an internet connection.
I had my Windows Surface in airplane mode while traveling. After I was able to get to a location where I could connect, Logos started right up. Then later, I put my device back in airplane mode with Windows open so I could continue traveling. Then, after finishing my study for the morning, I closed Logos. However, Logos wouldn't close. It only presented the sync window. Then, once again, after I was able to get back into service, I turned off airplane mode, and Logos immediately finished closing. All of this happened in that exact order a second time for me.
I travel a lot. And I fly a lot. So, that's why this probably stands out to me. I don't recall having this issue as a consistent problem in the past.