I think it will be helpful if you can share more information about the versions of ArcPad and Server that you are on.
Does this happen occasionally or it has never succeed in sending edits to ArcGIS for Server for this layer? I will suggest looking around the logs in ArcGIS for Server for more information during the period where you try to synchronize.
I'm not sure if this is going to be possible with that data. From my understanding, ArcPad 10.2 needs to use a feature service in order to edit. This was introduced at 10.0, so I don't think your 9.3.1 data will work.