Sodas have 3 stallers, usually:

Aspartame
Citric Acid
Caffeine

Besides, both aspartame and caffeine can produce an insulin response, making you not only store fat, but also crave sugar like crazy.

When I did my fist induction, I cut it out cold-turkey to see if any of the things would stall me. Then I reintroduced caffeine, testing my blood sugar and the results on the scale and saw no problem. Then I tried just aspartame, then aspartame and citric acid (sugar-free jello), and when all the ingredients had been cleared, I went back to my diet coke.

Personally, I drink tons of the stuff. I drink about 2 gallons water, and about 2 liters (10 cups) of diet coke everyday, and it has never stalled me. If it has been working for you like it has for me, I see no reason to cut them.