The Z1 will hold a considerable amount of data onboard the unit itself, something like a years worth of data without the SD card. The SD card option was there so you could send the card off to DME or sleep doctor, but if you don't need to do that there is plenty of data storage on the machine itself. I have heard some issues with the machine that were caused by people inserting the micro SD card that were corrected when the SD card was removed, so I have never put an SD card in mine because there is no need to do it.
If you can get the micro SD card out of your Z1 somehow that would be the thing to do and then don't bother with one if you can get it out.
As far as what you're describing with the data software on the PC, I have occasionally had the same issue when I hook mine up to the USB on the computer. In my case it was due to the PC not recognizing that the Z1 was connected. So I just disconnected and reconnected with the Z1 powered up with the AC power cord until the PC finally registered the USB connection and then of course the software could then see the Z1. So just fiddle with your USB connection, and be sure you are also using the AC power cord so that the Z1 is powered up in the standby mode, without power to the Z1 it won't work.
As a side note to the PC software, it pretty much sucks rocks........at this point in time it will only give you hours of use and leak information, but no AHI information. They say at some point that the software will be upgraded to show AHI info, but they have been saying that for about a year now. Seems like HDM really doesn't care much about that project, and the same goes with developing the Android version for their Auto machine, currently they only have an iOS version for the Auto Z1 that only works with Apple. HDM makes a lot of promises that never materialize -- it's pretty disappointing customer service and follow through from a company with such an expensive product, it's kind of amazing they are still in business!
Good to know, I was considering buying one (Z1 Auto) for a travel unit. May consider a Transcend instead. I liked the smallness of the Z1 Auto.