I've tried using both the SDMInstaller for Mac and EOScard for Windows, both do the same thing. On the computer, I see the CHDK directory, but on the camera the directory doesn't show up as a directory; it shows up as a file. I placed the script in the root directory and it runs properly though. If I put it in the Scripts directory, I can't go there at all.
So you clearly have an SD card with an invalid directory structure / incorrectly created directory structure.
Camera can boot to chdk just fine, but it just won't save settings.
Because it does not have a CHDK folder to save it to.
Is it possibly a problem with the card? or a bug with CHDK on the SX110?
Anything is possible but it 99.99% likely to have something to do with how you set the card up. Yes - I know that's not what you want to hear.
So let's start with the basics :
1) How big is your SD card ?
2) What computer are you using to set it up ? ( Mac or PC ? Windows or Linux ?)
3) Give us the exact file name of the distribution file that you are trying to install.
4) Exactly what did you do to get the CHDK distribution on your SD card ? If you used EOSCard, it will format the card but not copy anything to the card AFAIK. Did you unzip the distribution file to the card or just copy it there ?
That's a start. This is solvable - it just may not seem that way as you wade through 7 years of documentation of various quality and freshness.