Guild Wars 2

There should be a way that those of us who were disconnected from the internet can rejoin our party in FotM.

I wholeheartedly second this suggestion. Whenever a player in Fractals of the Mists disconnects, the character’s last-known location is Lion’s Arch.

It would be far better if the player receives a new prompt to join his party in the Fractals of the Mists upon re-entering the game in Lion’s Arch.

If you disconnect from a dungeon, you can still join your party when you return.
But if you disconnect from Fractals of the Mists, you can never rejoin your party unless everyone comes back out to Lion’s Arch (and aborts the run).

+1
Yes it is very necessary for us. This is a very user-friendly solution would be.

Even if it is technically impossible to rejoin your party in their Fractal, it should at least be possible to be returned to the Mistlock Observatory to wait and rejoin them on the next one, if they manage to beat it without you.
(That way, you would miss out on the loot chest, but would still be able to continue.)