If I lose my central tile, do I lose the round?
There are four cases where you give up:


If you choose to give up (which you can only do before revealing the next adventure card).
If you reach an Open Space card with zero engine power.
If an adventure card leaves you with no human crew on board.
If you are lapped in turn order (i.e. the player in the lead loops around the board and overtakes you) [courtesy of Samthere]


While the most obvious place to have human crew is in your starting tile (and indeed it will always start with two humans in it, never an alien), if you have another crew cabin with humans in it as part of your ship then it doesn't matter if you lost the starting tile or the crew in it, you can continue your flight.