Hi,
I've had a similar problem recently, I added the feature class created from a shapefile uploaded to our Online account (including .prj) file to an online map for data collection using the Collector app, which I tested at the time and had no problems with.
My colleague has been out and about collecting data today, and none of the edits he's created have saved. (I made the rookie mistake of not allowing syncing, and the area he's in has very poor 3G coverage, so that probably explains that).
I logged into the online account to check if any updates were saved, and the map we're using didn't include the feature class as a layer. I tried to add it again from My Content, and the "missing spatial reference information" error message popped up. I deleted and re-uploaded, and the same thing happened. When I tried again it seems to have worked fine. All of these uploads definitely contained .prj files (an error messages pops up when you try and upload shapefiles without one), so I'm wondering if there may be an issue with the process of creating feature classes from shapefiles. Is this a common problem?
Thanks
Gareth