We have to recommend having your Honda Civic inspected by either a Honda dealer repair center or reputable smog check test and repair center. Each of your vehicle's emission monitors have strict input parameters which must be met before the emission monitor test is initiated. For example, if the your Civic's engine never achieves closed-loop, the Catalyst monitor will not run. Or, should the ECT (engine coolant temperature) sensor indicate an irregular engine temperature, the air injection monitor may not initiate. It's possible that neither of these two conditions trigger the check engine light to turn on, but they will stop the drive cycle from making the required monitors ready. Having an auto repair shop attempt to complete the drive cycle in-house (on a dynamometer) will allow them to monitor all system parameters while the drive cycle is in progress. They can pinpoint what may be causing your Honda Civic's emission monitors to not set.
Related Links:
https://www.smogtips.com/smog-question/3580/2005-Honda-Civic-O2-Monitor-Not-Ready-After-Replacing-Oxygen-Sensor