Hi Everyone

I have the Deore SLX groupo (11-34) on my 2010 Giant Anthem X0 (about 300 miles of use) and I have this puzzing problem.

When shifting from the 11 up to the 34, shifting is normally crisp, except for the middle cog (gear 20). I can hear it trying to shift up but it won't go. If I shift again, it jumps 2 gears and shifting to the 34 just fine. So I'm stumped because it's only gear 20 that hesitates.

Has anyone see this before?

Soundes like you may have a little slack in the cable. Sometimes as a cable stretches, you first notice shifting irregularities in the middle cogs. Shift the rear derailleur to the smallest cog and check for slack. If you have some,turn the barrel adjuster on the rear derailleur counter-clockwise about 1/4 turn, and ride-test to see if that fixes your shift problem. It may take a couple times of small adjustments to get it right, but I caution about large adjustments, which can cause shifting to change for the worse. Fine tuning takes patience, but is rewarded when done properly.

I've been doing that, moving the barrel up by 1/4 adjustments. I've gotten it to shift really well except for the middle cog. If I get the middle cog to shift normally, it throws off the other cogs.

It sounds like you have done the 'normal' checks. Now you might have to do some 'off the wall' checks. It could be a problem with cable sticking at the wrong time. Look for any areas of cable that may be kinked, or misaligned. It might be a problem with your shifter in that ONE position. Beyond that, you may be in store for a trip to a good LBS.

Good point.
I should add that I have 2 sets of wheels and I have the exact same problem on both rear wheels.
I installed a new chain this morning, same result.
So what I haven't changed yet is the cable and housing.
The rear hange is as straight as can be.