Hi,
I witnessed such failure in general but not with DropBox per se, the cause was installed Antivirus with settings to inspect encrypted connection, it will hijack HTTPS sessions and replace the certificate with its own.
To identify/check/verify this guess/theory, ask one of the failed client to see if he visited a site like delphipraxis.net, then what does his browser report the certificate issuer ?
the real certificate is issued by
Code:
Common Name (CN) Thawte RSA CA 2018
Organization (O) DigiCert Inc
Organizational
Unit (OU) www.digicert.com
If it was replaced by Kaspersky or other
AV then the issuer will be different and/or the path of trust chain that leads to a root certificate is different.