Because they don't know how to power such an object for that long, can't guarantee a minimum reliability over that long a haul, and can't afford to build it in the first place.
And, even if they stayed put, there should still be evidence. Radio, ect.
We've barely begun to listen. RadioAstronomer can give you some hard numbers on how many star systems we've checked thoroughly for radio transmissions.
If intelligent life were as common as some people think, we'd know by now.
If we'd found it by now, it would mean that the galaxy is bursting at the seams with civilizations.
How would you know?
Because they don't know how to power such an object for that long, can't guarantee a minimum reliability over that long a haul, and can't afford to build it in the first place.
Building cost is certainly a problem, but not power. The ship would be coasting most of the way. I think the real reason is that after a generation or two, the bathrooms get really yukky, and everyone would prefer to die rather than use them.