Never is a really long time. XBox 360 will output 1080p over Component.
There is no such physical limitation.
Perhaps very bad component cable could degrade the signal, but not prevent.
Just for clarity, in the consumer equipment context, when you say "1080p," it always refers to 1080p@24fps?
Whereas 1080p@60fps outside of maybe inside or in facility professional broadcast studio distribution (or "3G"), is not normally used by consumer gear?