That error is coming from the local network client, and seems to indicate an issue with the network connection. Especially since this doesn't happen on all devices, it looks like it may be caused by the network connections on those affected devices. Is there anything on those network connections that may be interfering with the calls to api.dropboxapi.com? E.g., any proxy, firewall, etc.? Are the devices able to access the Internet otherwise?
I see, thanks for the information. That is certainly unexpected, as you're able to make calls later in the process, especially since the calls for checking for a folder go to the same Dropbox hostname as the ones for creating new folders.
Does the app do anything different for the first call? E.g., is it perhaps running before some other setup completes, or is the Dropbox client object handled different?