I have to agree with the above person in that I think it sounds like a timing problem with your PC, because a rapid change in date/time could cause the other issues you're experiencing:

For example you said about your network card and WiFi both reset* which could be because when the date/time changes it forces both network adapters to refresh their IP address (by default they'll be getting an IP from your router and they'll refresh that every X hours which would get triggered early if the time is drastically changed).

Normally I wouldn't expect you to actually get disconnected from the network when they refresh the IP as you'd generally get the same internal IP again, but if the game has a problem because your local PC time changed, it might very well also disconnect you as an anti-cheat measure.

Do you know of any sort of software on your computer that is attempting to keep your clock in sync? If so I'm guessing that's where your problem is because I've personally seen it before where sometimes the server they're getting the time from is wrong (just the wrong timezone would explain multiple hours out) and rather than question if the clock is actually meant to change by X hours, it just does it and perhaps that's happening here.

To the best of my knowledge FFXIV doesn't try and change the system clock, and if you're running on Vista or higher (probably?) and haven't disabled the User Account Control, by default the game wouldn't even run be running with administrative privileges so even if it did try to change the time, it would be unable to do so.

*Are you actually using both network card (wired?) and wireless simultaneously as that might be a problem unless they're both connecting to different networks and your computer is acting as a router for whatever reason.