On a CTX 670 with PRI card, what would cause a DID number to sometimes to ring the front desk instead of the extension?

Thanks!

Hard to say. My only thought is that the carrier is not sending the DID digits in some cases and the CIX uses the intercept value instead of the DID.
Also could be a protocol settings problem. NI2 is typically the most common PRI protocol used, but this is a conversation to have with the carrier to confirm how they are configured.

There was a forward placed by the carrier that once removed killed the DID and then we could get the carrier to fix the incoming DID to the PRI.