Did you find a solution to your problem ?
We have the same error and log message (max number of replica), and apparently, the replica created by the collaboration for one item is not removed.
We can see them in rest/services/folder/service_name/FeatureServer/replicas
Even after unsharing/resharing the item, after 6 synchronizations, the collab fails to sync again.
I did get a resolution on this a few weeks ago by visiting the product islands at the Esri Dev Summit in Palm Springs. In the end it turned out to be nothing more than a browser cache problem. I used a different computer than I had the first few times, so of course the problem did not reproduce when I sat with the technician. Back when I first wrote this blog I did try several forced reloads of the web app, but I don't recall deleting all temporary files.
The Esri technician informed me that when you set up a partnered collaboration, what's different from a distributed collaboration is that there is only one data store in the cloud. Distributed collaborations have multiple data stores, so the data has to be replicated between them. Partnered collaborations are about setting up user accounts to access just one data store, so as soon as the other organization's editor makes the edits, they should be visible to your own map viewer because you're both referencing the same feature class from the same database.
I hope this helps.