In the diocese where I live all clerical appointments appear to be in the gift of the archdeacons insomuch that all applications have to go to them in the first instance. Therefore, if an archdeacon does not like you there is no way you are going to be allowed to present your case before the parish representatives and the bishop. For example, when I send an application or an enquiry about an appointment to my local archdeacon he does not even deign to acknowledge it let alone action it.
Now, arguments can be made for both the old method of bishops appointing clergy to posts and for the new method of parishes having the casting vote, but, for the life of me, I cannot think of one good reason why an archdeacon should decide. In fact, I can think of plenty of reasons why they should be kept out of the appointment process completely. They tend to be legalistic, bricks and mortar types, often referred to as bishops' attack dogs. The ones I have had dealings with have been singularly devoid of pastoral sensitivity, Machiavellian in the extreme and very willing to bear a grudge. Like so many in the Church of England hierarchy they are in power because their desire for power gave them the hardness of heart needed to push everyone else out the way to get it.