That does seem strange.
I think you have to set the analogue out to 'headphone', when using headphones, so you can't accidentally set it to 5.1 when using headphones. That could happen when using speakers, and could explain why the bass would disappear if using stereo speakers; but having to select 'headphone' in the analogue out box, means the card is outputting as stereo and all frequencies will be sent to that output, or at least should be.
Changing the number of audio channels should not make any difference. Just out of interest; does it also do the same for 6 and 8 channels?
How long has this been happening? Did it work previously, but is something that has started happening recently, or have you just bought the card?
If it isn't something to do with setting within the STXII's control panel, then it surely has to be a software issue and the likely culprit is Windows 10, assuming you are using that.
Best to check other settings in the control panel first, such as those under the 'flexibass' tab and the 'effect' tab
If it isn't anything to do with setting in the control and is driver or Windows 10 issue related; then Asus' driver support is terrible. Shocking really that they can continue to sell what is their flagship sound card for £200 and not bother to update drivers for almost 4 years. Uni Xonar drivers you have tried from Maxedtech, do help with some issues, but they are still based on whatever drivers C-Media releases.
I suppose the only thing you could do, would be to try older Uni Xonar drivers and see if anything changes, or maybe try Windows 8.1 drivers. I've seen people in the past use 8.1 drivers when there none for Windows 10, or they didn't work properly.