So after months observing this, my conclusion is that the problem is with automatic switching from day/night of the ICR. With ICR in auto, I get all the symptoms described in the original post, most importantly the camera is removed from the list of available cameras on myDlink/Dlink app and doesn't generate push notifications. With ICR on "schedule" mode, this doesn't happen. The camera (two cameras for me) still reboot about every other hour for no reason, making it unavailable on myDlink/app for about 30 seconds, and interrupting the continuous recording. This is a problem, but not as bad as the other problem described above.
Both cameras that exhibit this are currently on 1.12 and this did not happen in either camera in earlier FW, but earlier FW's had a bug with not sending emails and I prefer to receive emails than to resolve this by using an earlier FW. (I have a third camera on 1.02, it doesn't have this problem, it doesn't reboot, but it doesn't send emails.)
I don't plan on contacting Dlink because I can live with this as it is, but I would certainly appreciate if anyone affiliated with Dlink on this forum pass the info along so this can be fixed.