You might want to run some code that works "just" the shift registers first, to be sure nothing else in your program is "upsetting" the flow. Use any of the examples at the site, then let them run a sequence for half an hour to see if there's anything irregular going on that isn't covered by the tutorials.
Also, post a pic of your breadboard - I've seen 595's misbehave due to wiring and code.
Otherwise, unless the chips are "factory sweeps" they are completely reliable to do as they're told 