Before advancing to the next season I submit offers to all of my upcoming free agent. But none of them stick with the team once I advance the season and click OK on the dialog box warning that I will lose any of my upcoming free agents to free agency. Is there another step that I must take before advancing the system outside of offering contracts to them?

You need to be re-signing them during the season. I'm not sure at that point that any further signings will happen except for CPU teams.

Thanks for the response. Perhaps the warning should be a bit earlier, like a last chance during the season after a certain week?