Not even that; relativity doesn't allow a single special frame of reference. There's no such thing as universal "time elapsed since x". Putting the clock in space would be as arbitrary choice as putting it on my roof (albeit definitely more practical).
I think the one who solves this problem ( at least for humanity ) would get a Nobel.
After the humans will wander thru space ( at some time - very probable), there will no time reference, but only time intervals ( like, day on a spaceship has 24h , etc ). So in this case, you would measure 86400 seconds and call it a new day. No more leap seconds, etc.
Now the UNIX makes sense: count seconds since a certain event in time and meajure from there on, internally. Want to display it? Then use special computation to render it in the format ( read timezone, add relativistic skew, etc ).
