It sounds like the clutch needs to be adjusted. I had to do this on my old HRM215 mower (which I am working on now). I also have an HRR2168VKA which has the same drives as yours. Yours has a Cone Clutch Variable Speed Transmission. Check the adjustment.
I hope this helps...

Look at your manual for the cable adjustment. That is basically a hydrostatic transmission. If the cable for the clutch is too loose it will act like a slipping clutch.
So, looks like a easy adjustment you may need 2 10mm open end wrenches.

Thanks for the prompt reply (s), I will make another adjustment to the cable as soon as this thunderstorm passes.

OK, so I adjusted (tightened) the clutch cable. The handle that operates the speed is now much harder to push, but it still no power going uphill or going thru thick grass. The engine has plenty of power, and the wheels are not spinning does the clutch need to be replaced? Is there a way to add/replace the fluid in the transmission?

First, md.stamen. What are you trying to say when you said that their tranny was pretty much a hydro tranny?

If there is a clutch it's nothing like a hydro Tranny. The propulsion system in my HRX uses the hydro fluid at varying pressures to drive a belt that drives the wheels. No clutch.

To the op, I'm thinking you have the smart drive system. If so they do use a cone type clutch that shouldn't need replacement but stranger things have happened I'm sure. It could be the tranny all together. Hate to say it but it sounds like you have done what Honda would recommend before looking at the actual transmission itself.

bsmith. I suggest that you go back to school and learn about Honda Transmissions before you make a ass of yourself.

Show me a diagram for a clutch on a hydro HRX.

Here's one, dont see a clutch.

http://www.planopower.com/store/honda/harmony_hydrostatic_transmission.php

Help me out here boss. Don't get all snippy about it.

I opened my HRX 217 manual and looked this up.
Page 14-9 Says. When the clutch lever is released the pump bowl pushes the neutral valve open and the oil flows in the reverse direction. No oil flows to the pump motor, so the lawn mower does not move.
Call it what you want , but Honda says clutch.
You guys need to just have fun and enjoy life.