Can you post more details of your environment? There are many hundreds of permutations of database, GIS software, and OS versions, each with their own quirks and configuration requiremetns.
What version of operating system is the GIS Server, Database Server, and the client installed on (where client is either a web browser or desktop ArcMa)?
Are you using GIS or Web Tier Authentication? Are you using a Web Adaptor? If so, what flavor of web server? IIS or Apache? If Web Tier, are you using Windows Active Directory for security? LDAP? SAML? If so, are you enforcing PIV credentials? HTTPS (hope you are)?
What flavor of database? Oracle? SQL? Is a domain service account starting the database? Have the right permissions been assigned to the feature class in question? Has the right group (role) been assigned to the rest service? Or is this a service based of a hosted service (FGDB in the server data store)?
It would be very helpful if you could post exact steps to reproduce....think like you're instructing a robot to make a jelly sandwich. I say this tongue in cheek, I probably still won't know what your problem is, but including specific and environment details will likely get your question answered quickly.
