Looking forward to your support .
We have one more desktop where we are facing this issue.
The ArcGIS FDO error code corresponding to this is "FDO_E_SE_OUT_OF_CLMEM", but unfortunately I don't have a good description of what this really means. Since the favorites load on other machines, it doesn't seem likely that there is a problem with the favorites repository, of course it is something local to the machines having troubles.
How is the system memory looking before the edit session is started, is there sufficient RAM and/or swap-space available on these systems? Could they be running out of memory? If that isn't the problem I would recommend doing a "repair" on the ArcGIS and ArcFM installations, and check for any missing customizations that would need to be installed on these machines.
If none of these suggestions is helpful, let us know, I can create a support case for this, and we can pursue the matter further. Also, we can check with ESRI for more details about the specific meaning of that error code. Of course it has something to do with being out of memory, but what kind and in what context, I don't know.