How do I fix my "OLD" glass door knobs?
Three options:


Buy vintage glass knobs and shafts.  These are widely traded on eBay as of this writing at about $40/pair.  If it survived 50 years in a different house, chances are it was well made.
Buy better quality reproduction glass knobs.  The item you pictured is looks like plated brass.  Get the solid brass stuff for more money.
"House of Antique Hardware" (http://www.houseofantiquehardware.com/) can get you set up just fine.  The cheap stuff is about $35, the good stuff more like $45 a pair.
Get reproduction or vintage cast iron or steel knobs.  These won't break, even with a hammer.


If you get glass knobs DO NOT OVER-TIGHTEN THE SHAFT.  It will contact the back of the glass knob and break it.  Mark the depth of the shaft before threading! Tighten your set screws properly.  Tighten set screws so they hit the flat, not the angles, of each shaft.  If the turning pressure is too high take the lock apart and find the problem (lubrication is optional, but chances are a spring is jammed in the works or something is bent).  These locks are simple to take apart.

The extra effort to use vintage is worth it: the house likely won't look right with modern knobs.  See also Fixing vintage glass doorknobs with loose glass to brass connection