Thank you for posting. My apologies for the late reply.
I'd like to get additional information to help identify what is happening here.
1. Are all the Macs on the same OS X version? What is that?
2. What browsers are they using and what versions are each of those browsers?
3. Are the three Macs in the same location? Are all the clients on the same local network, or are there some remote clients as well?
4. What does the client see when the data changes aren't accepted? How often does this happen? What is the client attempting to do when this occurs?
5. Do all the Instant Web Publishing clients have the same privileges? Are they all using the same layout(s)?
6. Have you been able to test this solution using FileMaker Network Sharing? Does the button behave in the same way?
7. What, exactly, does the button do? Did it ever work on a Mac?
I know it has been several weeks since you posted, so if you have resolved this issue, please post the resolution here so that others may benefit.