Is there any way to SAVE your game in this demo?
If you are asking about an in-built save feature then no.
??? Sorry for asking the obvious but did you select the right program?
Try restarting CoSMOS if that still doesn't work I will take a look at mine again as they could have released a micro patch.
I tried running CoSMOS as both 32 and 64 bits(64 bits Windows 7 here) and no matter what I do, when I load ReckoningDemo_time.CT I just can't edit the Value field, it shows up as ??.