no its not impossible, here's what happened in the match-ups I've had against fizz as Ahri (because thats who I play the best with and am most comfortable with)
Combat normally goes like this:
I Q minions for cs fizz begins his engage sometimes with his E and lands straight on me if I have flash at this point I HAVE to use it because if not I lose a chunk of health, and the cycle repeats after Qing away on a minion. Now that I dont have flash unless I ult I cant dodge his next E even if I Q since it launches you forward, once i'm slowed he Q's to me or Q's to a minon to get away since his E already did all the poke, if he stays it'd be because either I missed my charm or he W's then can keep AAing or walk away since im on cooldown. At this point his abilities have done enough damage to either kill me or leave me really low.
On a side note: before level 3-4 I have noticed that there is a little struggle with farming but its not like I can just spam my Q and keep my mana so id have to get close enough to auto attack if I wanted to poke him away but then his minions would aggro on to me, id most likely miss CS and he could just Q onto me and deal damage to me with his minions until they reset aggro onto my minions then he backs up either way that fizz I mention was still able to cs all he did was wait until after I used my Q since he can just stand behind minions to avoid my E
TL;DR: Yes he pretty much dodges all the spells, burst champions and anyone squishy cant fight him, he cant be ganked either because he can just E away then back if he seriously needs mana, the only times i've managed to kill him is if my charm lands and my jungler happens to be nearby enough to engage with me.