Morgana

Depending on the enemy's skills as Morgana, it could potentially be a major threat due to her stun, ult and spell shield, preventing your target to get slowed or charm, pretty much rendering you useless.

Fiddlesticks

Pretty obvious, if you get close to him, he fears you, silences you and it's pretty much GG.

Brand

Being a squishy support, Ahri is obviously susceptible to burst mages like Brand, Zyra and Vel'koz. However if you can make them waste their spells and/or dodge said spells, there shouldn't be much issues.

Vel'Koz

See Brand for more details.

Zyra

See Brand for more details.

Sivir

Similar to Morgana, Sivir can spell shield your Charm meaning you wouldn't be able to proc Font of Life for your carry to heal off them.

Pyke

Not much of a threat, however due to Pyke being Pyke and Ahri being squishy, it wouldn't make much sense not to put him here as somekind of threat.

Nautilus

Due to the engage tool Nautilus has and the fact that Ahri is pretty immobile pre level 6, Nautilus along with the other engage/hook champs are extremely dangerous opponents.

Thresh

See Nautilus.

Blitzcrank

See Nautilus.

Alistar

Twitch

Due to him being able to go invisible, Twitch can potentially be a hard target to Charm. However once Oracle Lens and GLP are available, he becomes less of a threat.

Braum

Braum can shield himself from the damage of both you and your ADC, along with making sure his carry doesn't get Charmed earlier on.

Janna

Due to her disengage tools, Janna can be somewhat of a pain to deal with, though she shouldn't have much kill pressure in general, she just makes your life somewhat harder.

Poppy

Poppy can stop you from using your dashes, meaning you're very likely to die if you're trying to engage on them.