A 404 failure usually indicates that the computer isn’t able to resolve the . Could you try pinging this alias from a computer with the failures? It could be a DNS issue if you are using a DNS alias for the BES Server.
If the ping is successful, try copying the full url (http://:52311/cgi-bin/bfgather.exe/actionsite) into internet explorer on the box and see if that resolves or not.
If the url fails, your BES Server likely isn’t propagating the actionsite correctly for some reason. Support should be able to help you figure out what is going wrong, you may want to raise a support call.
Talking with support… if the BES Server runs out of disk space it won’t be able to create the latest versions of the actionsite and the BES Clients will receive 404 errors trying to gather the non-existent data. Try clearing up disk space and then take a new action to propagate the actionsite.