Why does everything I try to influence turn stubborn after four attacks?

Use a different attack each time.

I do.

Stubborn is fine, it's willful you want to watch out for.

They turn willful about 3-4 attacks later.

What's your Charisma? How many attacks are you using? What's your skill level in Influence? Are you using a dramatics performance enhancer? If druid/mage, are you in meld? What mobs are you having trouble influencing?

12 Charisma. I'm using Begging and Supplication on friendly denizens. I'm up to Supplication. No Dramatics. I'm not a druid or mage. I have trouble influencing almost everything. I've only successfully influenced the Serenwilde treetop elfen and faelings since leaving Newton.

Some charisma boosts:
being a Moonchilde
beauty karma blessing
netzach in High Magic
being present at a Herofete
truefavour from a God

Some begging boosts:
wearing sandalwood oil
wearing tawdry clothing
having a beast trained in Influence Begging

There are others, but these are the easiest to get. Besides more training in Influence and Dramatics, that is.

Performances also help, eg PERFORM VAGABOND. Vagabond is fairly high up in dramatics, but sycophant and bully are pretty low down (empower and weaken, respectively).

A throne is also a fairly-long term option you can work for to boost charisma. They are costly (think 50k gold +) but they last for like a RL year or longer. Simply SIT ON THRONE after every login/death to get +1 to charisma. Just make sure you put it in a spot you can ensure access to.

In cooking, what do juices and ciders fall under?

Also, the 0-lesson skill in dramatics is PERFORMANCE. PERFORMANCE ON, while it won't directly boost your begging, will make your life a little easier by trading mana for ego.

In the same vein, Mercy enchant (mana regen) and beauty enchant (ego) help. Leaving the room that the denizen is in and then returning is an instant +huge amount to their influence resistance. If they get a "So what do I care?" attack in, I'm pretty sure that raises their resistance a substantial amount as well.

Also, since you're begging, try aiming for the lowest prestige possible without being buck nekked. Tawdry/tattered clothes give negative prestige (good for begging). All other influences you want to look as rich and awesome as possible. Lastly, if you're at a fairly low level, don't expect to be able to influence higher level mobs. I suspect your 'influence damage' is at least partly affected by character level.

Nothing, at the moment. They were like tea before brewmeisters were introduced.

Mana Regen is Perfection. And I was under the impression that Performance traded really little mana for ego to the point that it wasn't worthwhile? Not sure though.

IIRC, at trans dramatics it's like 200ish mana to ego per tick, I think?

So I can't design juices and ciders?

Sadly, no. Unless they're a side item on a platter, but I'm not sure if that'll slide. Could always try.

Oh goodness, I fail. Yes, perfection is mana, mercy is health. *fails it* Performance is lv 1 mana drain granting ego regeneration proportionate to your skill. If you have perfection up with no other sources of mana drain, I'd say it's always worth it.

If one uses a changeling cameo to go from Illithoid to another race, what happens to the illdrain ego if you have some before you change?

How do I resign my position as a professor of a collegium?