Does Final Fantasy Tactics have noticeable slowdowns even on the iPhone 4S

The permanent boost from effects like Ramza's skills and the lectures of a Orator is only a fraction of the change you see during battle. Ramza may be able to raise a unit's Bravery by 5, but the permanent boost is only going to be 1. The same goes for the Orator's skills that raise or lower Bravery and Faith (and, to point, the Orator is the only way to boost Faith in this fashion).

As such, if you want significant boosts to your Bravery or Faith stats in either direction, you need to be using the abilities to alter your Bravery and Faith stats repeatedly during battle. In due time, you'll see the impact. Keep in mind, however, that with the permanent stats: a unit who hits 5 Bravery or lower will leave your army out of fright, while a unit who hits 98 Faith or higher will leave your army out of religious enlightenment (this latter one means the actual Faith stat, so being under the "Faith" status effect doesn't cause this). So be wary while you play around with these and make sure not to go so far as to lose your units!

When just dealing with success or failure, the important points are as follows (see this FAQ in section 00err1):

Each character contributes a number of "Work Points" based on three factors:
 * Current job
 * Bravery & Faith
 * Exp Level

From the Final Fantasy Tactics page on SquareHaven:

To increase the success of any job, send the maximum amount of units (three). Also, some jobs can be performed best by certain classes or a certain type of class (e.g. physical or magic), which the bartender will sometimes allude to when the job's proposition is selected. (In addition, the correct type of job can be deduced sometimes by reading the proposition.) Specify the maximum amount of days. Finally, recall your deployed units when a job is completed as soon as possible.

So, try to deduce the proper classes to use, and follow the other guidelines you've already been using - send the max number of people, for the max amount of time. Maxing out the time doesn't appear to increase the odds of success, but it does help you to get the best rewards.

For more information, consult this FAQ, specifically section "00err2." There's a list of all the errands in the game, the jobs that they prefer, and some tips for each errand for earning "bonuses" based on the characters Bravery or Faith stats.