I have run into a problem where I install a networked printer on a computer as a local printer and once I reboot the computer the printer disappears. I made sure the printer was available, and I could reinstall the printer, but as soon as I restarted the computer it would disappear again.
I realized the problem had to do with the share name. Even though I was not sharing the printer through the computer I needed to have a share name on the printer. Usually one is provided during the install, but I have found that occasionally the field is blank during the install process. If one is not provided, usually all you have to do is click the share button. Once you do this, a name usually appears. Then just click Do not share printer.
Here is a screen shot of the install showing the share name blank.
As you can see once I click Share this printer a name is populated. You can change this to whatever you want.
You can see that when I click on Do not share, the name stays populated.
I have had this problem on 3 different computers, and this fix has worked every time.