On the one hand, it's crazy dangerous. There's nothing more dangerous you could do on a computer than give an untrusted program administrative access to your computer. There are no limits to what the program could do; install rootkits, delete your files, add your computer to a botnet. Anything.
On the other hand, that's exactly what you do every time you run a program as administrator. So, if the program is going to do something nefarious, it doesn't need to save your password. It just needs you (the administrator) to run the program with elevated privileges. Which you probably already did before you got to this point.
As for what the additional danger is in allowing the program to save your password: Windows internally stores your password as a one-way hash. Nothing, not even Windows, can retrieve your password until you type it in yourself. But by providing the password to this program, now you're additionally storing it either plain-text or using reversible encryption. So you've decreased your level of safety by one notch. Not a ton, but it is indisputably lower now. And if they do this bit poorly, then all the worse for you.
Next, Windows actually encrypts certain key bits of your security profile using your login password. These bits are not accessible to anyone or anything until you've provided your password to log in. This is wonderful and super and all that, but it also means that nothing can impersonate you (not even this backup program) without your password. And in particular, scheduled tasks can't run as you without your password. This is just the way Windows was designed; it has nothing to do with this backup program.
And finally, since this issue with scheduling tasks to run as a user is a known problem in Windows, there's actually a core system function for storing your login credentials specifically for use running scheduled tasks. This means that the backup program doesn't have to store your password, it just has to tell Windows to do so. So it's unlikely that this backup program is directly doing anything with your password, they're probably just handing it off to Windows to use with its built-in task scheduler.
So in that case, the safety of your password would be more of a function of the safety of the Windows task scheduler, not this backup program.