I've experienced a lockup issue as well that sounds similar to this. In short, the game input will literally lock-up for 30 seconds to 3 minutes at random times. All animations will play, all other characters will move around accept my own because my input is frozen. I can move my mouse, but the cursor will not change (the cursor is also locked). Mouse and keyboard inputs are totally locked. In other words: it feels like the game is running and that you are being disconnected, but you are not.

This has happened to me in the following circumstances:
- Running Dusk Vigil at the final boss. My inputs were locked for 2 minutes.
- Running The Vault between the first and second boss. We were pulling ordinary mobs but my inputs were locked for 2 minutes.
- In a story instance in the Sea of Clouds (fighting goblins with Alpie), my inputs were locked and I died before I regained control. I restarted in instance and it was fine thereafter.

I have also heard this reported by a player whilst running Dusk Vigil. Her inputs were locked prior to the final boss fight. We waited for a couple minutes for her, and she reported it after her inputs were restored (this happened in the first circumstance cited above).

Some thoughts on this issue:
- It did not occur during early access. These events have happened only since the patch on June 30.
- It does not seem connected to a specific class/job, but all three of my experiences have occurred within an instance.
- I have not experienced this issue during a teleport like the OP.

Technical thoughts:
- My video card drivers are up to date
- My DirectX is up to date
- The remainder of my PC functions normally and no other program is affected
- I am hardwired into my internet and the signal strength is not related to the issue
- Zero PC memory issues from what I've noticed during these events
- I often run Skype while playing for FC voice chat

There is, to my knowledge, no setting in-game that would account for the input lockouts, and I have seen no other thread on it. I'm not sure what was done during the last hotfix, but the issue is prevalent. I wish I could specifically reproduce this issue, but there are too many variables to be able to test without a dedicated group.

I would love to hear some response if SE has encountered the same issue. (This may also be relevant to the "In-Game Bugs" forum, but I'm placing it here because the OP's issue sounds identical to my own.)