I came across your post cause I ran into this error today.
Not sure what worked for you but restarting the SyncTools and SyncToolsEx service seemed to have resolved the issue for us. Just wanted to put it out there in case it helps someone else.
Has anyone found a solution to this yet??? My offline download fails on both Collector apps due to this same "GP Service Response Error." This is the first time I have experienced this error and I've changed nothing with my workflow.
