Bicycle Mechanics - Rear derailleur problems

I'm stumped. I took my bike to the LBS and they couldn't find a problem so maybe you folks can help.

My 9 speed Ultegra rear derailleur hesitates or doesn't shift when I'm shifting from cog 3 to 4, 4 to 5, 5 to 6, and sometimes 6 to 7. Same thing when going the other way. The cogs don't look worn. Happens on large and small chainring. This has been a problem for a few months.
I've cleaned and lubed the drivetrain but it doesn't help. I've adjusted the cable tension and tried turning the small barrel adjuster (1/4 turn increments) near the rear der.
The chain isn't stretched and has ~4000 miles on it.
The bike has ~11,000 miles.
Is the problem in the shifter?
Is it time to change the chain even though it isn't stretched?

Thanks for your help.

Have you changed the cables and housings? May be time to replace the chain and cassette as well.

Try cleaning the brifter

My money's on gunked up cable housings, in particular the rear loop. Try cleaning or replacing housing and maybe cable. Should not cost you more than about $5 maybe a little more if the LBS does it. Try that before other more expensive solutions.

I would check the cables and housing. I had the same problem a little while back and there was some crud buildup in the cable housing that was slowing the shift transition.

Have you checked the derailleur hanger alignment? Bikes with 9 and 10 speed cassettes are more picky about derailleur hanger alignment than bikes used to be.

I doubt you have a cable or housing problem because that usually causes hesitation when shifting into a smaller cog but shifts normally when going the other way.

I would defininitely check your derailleur hanger. my bike was doing the same thing. park tools has a derailleur hanger tool that'll bend it back into shape. maybe your LBS has one. if your hanger isnt replaceable, then that might be your best bet

Thanks for the suggestions.
I replaced the cables about 500 miles ago.
I'll check for a gunked up cable housing. Those weren't checked or replaced. :o

Replace housing when you replace cables. Not a bad rule to follow and it's not gonna cost much more than doing cables alone.