Hi Scotty, I have a 2004 civic lx manual purchased new. I only have 57700 miles on it. A couple of years ago (at less than 50000 miles) I got a P.O.135. HO#2S-11 code. the bank1 sensor1 o2 heater electrical circit heater circuit malfunction. I changed the sensor and the check engine light went out. Coincidentally I noticed my Cruise control went out around the same time. I read that sometimes the cruise won't work until the check engine code is removed. I have changed that o2 sensor several times since then and every time I try to use cruise ,the check engine comes on and the po135 code comes back. I can keep the check engine light off as long as I don't try to use the cruise. How can this be? Are these two related somehow? Thanks
Sounds like you have a short in your wiring harness somewhere. Your gonna have to get a mechanic to send test signals through and track it down.
This is a real "head scratcher" and I've hesitated to "weigh in" on it but maybe a "train of thought" exercise will be helpful in your diagnosis.
So, Submitted For Your Consideration.....
The HO2S1 (sensor) has a few things in common with the Cruise Control. Both receive battery voltage from a common fuse in one part of their circuits. (not saying it's a fuse, just rambling on).
The wiring to both are "bundled" in the "Left Side Engine Compartment Harness".
Both share at least one connector.
At first I suspected the harness ground may be the culprit but the computer provides the ground to the HO2 Sensor Heater Circuit, so that's out.
Let's look at the Left Side Engine Harness.

So the P0135 code means there's a problem with the "heater side" of the sensor and that has nothing to do with any "common ground" between the HO2 sensor and the Cruise Control.
The P0135 code means the HO2S1 (sensor) is taking "too long to heat up" and if it isn't a "Ground issue" it has to be a "Power Side issue".
Is engaging the Cruise Control Actuator Motor somehow "dragging down" the voltage to the HO2S1 (sensor) and causing the P0135 code?
How the heck could you tell since you have to be driving the Civic to engage the cruise control?
Here's a thought but you'll either need a multimeter with long leads or have a cheap Harbor Freight multimeter that you're willing to "clip" under your windsheild wipers so you can see it as you drive.
Unplug the HO2S1 connector. Set the multimeter in DC mode, 20 volts range.
Since the PCM controls the Ground. You'll always have Battery Voltage (12 volts + or -) going to the HO2S1 heater socket in the connector.
So secure the negative probe of the multimeter (black wire) to the negative battery post connection (real good, you'll be driving). (If it's a $6 Harbor freight one you can use a vice grip)
Then probe the HO2S1 "Heater battery voltage socket". It's going to be #4 in the picture. (this ain't rocket science. Use electrical tape if you have to and you may have a better connection by "backprobing the connection at the #4 socket and taping it)
It's going to look like this:

Then drive the Civic. Observe the voltage without the cruise control engaged.
Then engage the cruise control.
Does engaging the Cruise Control "drag down" the voltage at socket #4?
If it does, at least you can determine "What's Happening" and maybe by looking at the Left Side Engine Harness and its connector(s) for an issue you can determine "Why it's happening?"