Here's my personal opinion, YMMV.
I was on Atkins in 1999 then again, strictly, in 2003. Restarted in 2008.
In 1999 I let myself have basically unlimited diet caffeine-free soft drinks, primarily diet pepsi. Generally 2-4 a day. I had carb cravings the entire time but I still lost over 100 lbs. It was hard though, and I was unhappy.
In 2003 I limited myself to 1 caffeine-free diet pepsi a day, with my supper. Still had carb cravings, still found the diet hard to stick to. 2004 I forsook Atkins then regained all the weight I'd lost plus a bunch more. Stuck with caffeine-free diet sodas though ~ I've never gone back to full-sugar soft drinks. Gross.
I restarted Atkins in 2008 and forswore aspartame this time. No diet soft drinks. I haven't had a single sip of one since August. NO CARB CRAVINGS. 100% on plan. Haven't found it difficult to stick to. I'm not a research scientist so I can't prove causation but I can observe correlation.
We're all different. For me, completely eliminating all processed foods and drinks, including aspartame and diet soft drinks, is the key difference between this round on Atkins and the two previous ones ~ and it's working great for me. I think diet drinks don't derail everyone but I think they hurt me, so I avoid them.
Actually ~ I did have one sip of diet pepsi a few weeks ago and it was SO DISGUSTING I had to spit it out ... your body really does adjust to not having it.