Sometimes it's actually a die production error!
Don't worry, they also called me crazy when I conducted an experiment by switching all games at my table to dice exclusively made in ways that minimize their potential for bias for 3 years just because I wanted to prove to them that the reason it appeared I rolled more critical hits than everyone else combined was because I am the DM and am rolling more attacks than they are as players, even collectively, and not that I was using biased dice.They called me crazy when I would pick up a handful of dice and threw them, taking the highest few. Well they'll see, oh they'll see!
I could be completely wrong, but doesn't it say you have to use the new result? Anyway, that's how I ruled it when one of my players rolled two 1's in a row with his halfling. I also want to note that rolling four 1's in a row is a very impressive feat.
Halflings Luck lets you re-roll 1's.
I rolled 4 1's in a row the other night...So of course I failed. At some point, even a halfling's luck runs out!
Just wanted to share.