the initial readings are correct (~23C / ~25% Humidity)
Over about 15 minutes the readings drift (~32C / ~12% Humidity)
A quick power cycle does not reset, a long delay does.
This indicates to me that there is some self heating, but I'm not seeing anything about layout or self heating in the data sheets.
We have tried to solve through firmware, by re-zeroing all values each time through. Does not affect drift.
I am not familiar with this sensor but the datasheet looks nice. I have a few things you could look at:
How are you powering this sensor? Can you temporarily power it from a separate battery (connecting the grounds together)?
Do you have a software filter or averaging algorithm in play? If so look at the raw values.
Have you looked at the SPI bus when the values are wrong? Are there other SPI devices that might be interfering? If so, can you remove them?
Did you take the protective tape off after soldering the sensor?
The datasheet says it has a response time of 6-8 seconds in fast moving air and up to 30 seconds in still air--are you reading it quicker than this? I would probably read this sensor every minute or even every 5 minutes.
By definition, a change in temperature will result in a change in RH. Some RH sensors have controllable heaters inside them (e.g. the SHT31), doesn't look like this one does.
It's possible (reasonable... perhaps?), that 32C and 12% RH is an accurate (within the error budget) measurement of the conditions at the sensing membrane after your system has achieved at steady state temperature. You could tape a small thermocouple to your PCB near, or on the side of the IC, and record temperatures from a cold start to get a sense of how much the PCB heats over that 15 minute span.
To get an accurate measure of RH of your process gas (air or otherwise), and not just of the small volume of gas near the face of the sensor, you might consider:
Design for better convection across the sensing element. Either passive or active (e.g. small fan). This should help reduce the response time of the sensor, and help drive the temperature of the sensing element towards the temperature of your process gas.
Use an alternative measure of process gas temperature and apply a temperature based correction to the RH measurement from your Honeywell element.
Adjust PCB layout (if possible), to reduce heat conduction/generation near your sensor. This app note from TI is a great resource.