Gabe, I'm sorry you are having this trouble, but, I'm afraid, the only person who could help you is the developer. No one else would have the solution, in big part because no one else seems to be having the problem, in the first place. As a professional software developer, I am always bothered when something is not working quite right, but I don't think I can help you. I even went on to download Sleepyhead (albeit, I got the previous version because I didn't have the time to deal with an installer) and looked at it. First, I should mention that after running it I did not experience the problem you are experiencing, but then, again, I did not go on to set it up completely and import CPAP data (my machine is not supported). What I saw is that the program seems to be using an array of shared libraries (Nokia's Qt, Minimalist GNU for Windows, GNU C runtime) but I didn't get deep enough to see if Sleepyhead uses the MS VCRT directly or by means of one of the dependent libraries. Did you have to install the VCRT yourself? Again, the answer to this simple question (i.e., whether the main code uses pure virtual functions) can be provided only by the author. In the very possible case where he did not, then the bug is in one of the libraries he uses, in which case you have a very slim chance of having this ever resolved.
Did you try reinstalling? Since I don't know whether the (un)installer has the option to clean up its settings, you might have to do it manually. You'll have to ask the author which Registry keys to delete to achieve that. An alternative is to install on another computer (to see if your chosen preferences/settings are what causes the problem) or under a different user on your current computer.
The author of Sleepyhead (Jedi Mark) is the only person who can really help you, you might try PM-ing him, or some other way of getting in touch, if you really need this problem resolved. Good luck.
Healthy, active, middle-aged man; tall and husky, athletic build; stomach sleeper; on CPAP since 2003; lives at 5000 ft elevation; deviated septum but a turbinate-reduction procedure helped a lot; regular nasal washes have cured my sinus problems.