O2 sensor light and rough idle problem on a 3.0 v8 engine

What is your question?

Engine idles ok at first start- rough after a few minutes or after you restart the engine. O2 sensor light on (front#1 unit). replaced sensor 4 times. Once with ford part and 3 aftermarket units. smoke tested system and mechanic tested for vacuum leaks and replaced distributor cap in case of crack. May be 2 problems but don't think so. Washed engine off today and truck ran rough. Someone thinks its the air bypass valve but why would the O2 light be on?. low miles on the truck (25000 miles)

What makes this problem better or worse?

idles better at first start up

How long has your 2003 Ford Ranger had this problem?

9 months