"I have never been able to keep my online tree synced with my FTM Mac 3 program for more than a few hours. Then it loses its connection every time."
A sync shouldn't run for hours.
I suggest you sync manually. Turn off auto-sync in FTMM quit and restart FTMM.
When you are finished with your work session, manually sync your tree. It should take a few minutes, depending on the tree size.
Always quit the FTMM application when you've finished with a work session.