So guess as step 1: Log into Server Manager and confirm the sync service is started and has available instances running.
Step 2: Can you make edits in AGOL, save them, close the browser, go back in and see the edits?
If not, then your issue is tied to the communications between AGOL and your backend so you'd need to examine what you pushed into AGOL. If yes, then can check next.
Step 3: If its allowing you to properly make live edits then all the pieces between AGOL, ArcServer and SQL DB are working correctly so the issue is specific to offline usage. Log into your REST services page and navigate to the Feature Service you are trying to use. At the bottom select the "Replicas" option. (URL looks like this: http://<servername>/arcgis/rest/services/<folder>/<service as FeatureServer>/replicas) Confirm that there are replicas being generated (these are the geodatabases stored on the server that match the SQLite DB's loaded to the users device at time of download or last sync)
If this page is blank then there is something wrong with your server configs that isn't actually building the ArcServer pieces necessary to match what the user is taking offline. If there are replicas here you can follow the directions on this site to confirm the edits that were being made in offline mode on the device actually made it back to these replicas. http://desktop.arcgis.com/en/arcmap/10.3/tools/conversion-toolbox/copy-runtime-geodatabase-to-file-g... If they did then it's time to call ESRI or perhaps someone else can assist because if the edits made it that far and simply didn't post back to your SQL DB aside from the Sync service we already checked above I can't say what the issue is.
Not knowing your backend configuration I can tell you 1 thing we saw (granted this was 2.5+ years ago) that might fit this. We used the Web Adaptor on an IIS web server VM in our DMZ with our Arc Server on a separate VM server behind the internal firewall. I put 6 testers in a room after they had collected 20 records each with between 1 & 5 pictures per record. I had them all hit sync at the same time. The primary bottleneck was by far the Web Server RAM. We had 2 of the 6 testers fail to sync but all they saw was a message that said something like "failed to sync" on the device and there was no good logs or anything else to determine the issue. Re-conducted the test while watching all servers performance in the environment and was able to identify the RAM spikes. Increased the RAM and re-tested and all users had successful syncs.