This is of interest to me, so I used the log parser at http://xivparser.com/summary/ to see what the actual rate of success is. I measured success rate using Hasty Touch buffed by Steady Hands II, which has a supposed 80% success rate. Here are the results:

http://pastebin.com/nDfPZme3

In summary, I got 938 successes and 216 failures out of 1154 attempts, which works out to a 81.3% success rate. It's actually surprising that it's higher than 80% because I was forced to use Steady Hands I for one single Hasty Touch step in a few of the chains which dropped the success rate down to 70%.

It's disheartening to get 5 failures in a row but keep in mind you tend to notice extreme cases more than mundane ones. I believe this is a true RNG and not a pseudorandom number generator which biases your chances based on past performance, so don't fall prey to the gambler's fallacy. If you think you are getting particularly bad rolls consistently, and that it might be a bug, then try parsing your logs to see what success rates you're actually getting and maybe submit them as part of the bug report.