This may be a long shot, but can you verify in your OS Advanced Power Settings that your network card is not set to power down after 30min of inactivity?
To get there in Win10:
Control Panel > Power Options > pick a power plan > Change plan settings
(on Edit Plan Settings screen) click "Change advanced power settings"
(on Power Options screen) expand the entry for "Wireless Adapter Settings" > "Power Saving Mode" > change all entries to "Maximum Performance"
Should look similar to this:
If the Power Saving Mode is set to anything but Maximum Performance, then the network card will power itself down after a certain amount of time "idle" in an effort to save electricity, and oddly enough, FFXI traffic may not qualify as "active" enough for it to stay at full power.
Let me know if this helps.
If you are on a laptop, there will be two entries for plugged in or not. I recommend changing both of them.
If a desktop, then should be only one, but I work tech support and have run into desktops that think they are tablets and have both, so it's worth double checking either way.
If you want to test if this might be the case without changing systems settings first, try to login all the way into the game for ~20min, then /logout and log back in. If you don't DC after ~10min, and then DO DC closer to 30min after the 2nd login, then it is extremely likely to be related to your power settings for your network card.
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Another possibility: There's been a lot of major network issues/failures in the past month or so, including Mediacom specifically:
https://whnt.com/2018/11/12/internet...north-alabama/.