Thank you for your post, and I apologize for the late reply.
When selecting "Open Remote", FileMaker Pro is looking across the networks for other FileMaker Pro files. It could be that one of the servers works only intermittently. What you may want to try is adding a few of the servers as an entry in "Favorite Hosts". Then, use "Favorite Hosts" to select the file. If you find one of the "Favorite Hosts" takes a long time to access, then the problem probably lies with that server.
If you have found a solution, please let us know what it is so that others who run into the same situation can benefit.