Redshift happens for a reason - specifically, when things move towards us, which compresses the light waves. Conversely, you get blue shift when things move away. If the universe is a "steady state" where it's infinitely large and old, then there's no reason for enough things to be moving towards or away from us to redshift or blueshift the light to the point that we can't see it.
Also, what DarkLink said. What you can see is actually a minute fraction of the electromagnetic spectrum, and there's a ton of energy in the states both "above" and "below" what we can see.