I am able to download maps for offline use with the collector app as long as I add the layer from my content. However, when I try to add layers from the arcgis online server, I lose the ability to download the map offline. I've tested layers within my organization and found that the map would not download offline unless the layer was in my content Is there any way around this, or do the layers always have to be in "my content" to enable offline mode? . All the feature service layers that I published myself already have sync, update, delete options enabled. The layers I am trying to add are also feature service layers. One of the layers is USA parks which was created by esri.
I would look to the provided Help Documentation link to verify you have prepared your data according to our documentation. If you find your data has been prepared according to the documentation, I would look to logging a support case with Support Services to better investigate the issue being seen with Collector and a Feature Service. Gracias, Colleen!
Prepare data for offline use
Your data has to either have archiving enabled or be versioned before it is published to server for it to be usable offline with Collector. See the link that Juan provided above for details.