Influences replenishes 1 point per hour. It does not refill on level-up. The maximum amount you can you hold is 25% greater than the number of skill points you have invested. So if you have 150 Influence skill points, you can "hold" up to 187 Influence points at one time (187/150). Even if the calculation shows higher value (in this case 187,5) game will round the result down.
One Influence point can be acquired at the cost of one Skill Point.