Network dataset has long field names. Field names in the network dataset's source feature classes can't be longer than 31 characters.
Solution
Replace any fields that have long names in the source feature classes with fields that have names that are less than 32 characters.
More information
To replace fields with long names, create fields with names that have less than 32 characters. Use Calculate Field to transfer field values from the old fields to the new ones. Delete the old fields. Open the Network Dataset Properties dialog box, click the Attributes tab, choose the network attributes that reference the long field names, and reconfigure them to reference the new field names. Finally, rebuild the network dataset.