Are you also the host, iow the actual server hardware owner?
Are you using the dedicated server launcher provided by FC?
And I hate to say this but before you do anything you should try without mods, then you can tell if the problem is caused by a mod. If it is a mod, load them back a few or one at a time to eliminate the one giving issues.
I run a private server, with mods on my own hardware (older computer) and the Dedicated server launcher, I have no issues. But I am using much fewer mods.