jonottawa saidI often wonder: why not try to resolve what is causing the anxiety instead of just medicating it? I hope you don't take offence to the question. A friend is dealing with something similar and seems to be relying on medication.
Ideally, one is doing therapy even if they are also using some form of medication.
One of the advantages of of the benzodiazepines (klonopin, etc.) is that they don't have to be taken regularly. Especially low half-life ones (e.g. ativan/lorazepam) can be taken only acutely to help with panic attacks or similar discrete onsets.
Anxiety can, in some cases, undermine a persons ability to function. Aside from the fact that they may not have time to 'finish' working through therapy while retaining their jobs, social relationships, etc., a key part of overcoming anxiety is experiencing activities that make you anxious and 'learning' that you don't need to be afraid/anxious. Anti-anxiety drugs can help get you over the hump so that you can accumulate those experiences.
Finally, while brain and mind are inseparable, some parts of the brain are more easily accessed consciously and thus dealt with via "psychological" means. Sometimes people may just have, for example, a hyper-active limbic system or some other low level system that biases them to high-anxiety. Therapy is still important in that case, but medication may help in ways that talking and working can't.
(For context on the above, I'm a neuroscientist who has dealt with some anxiety issues of his own and had quite a few friends who've dealt with the same. Academics seem to be a high strung bunch.

I'm not a psychologist or psychiatrist though, so I'm sure others could contribute more. )
@OP, regarding addiction: I don't want to say too much because I don't have ea lot of experience with that aspect in particular. It is my *non-professional* understanding that benzo addiction is slightly exaggerated as a problem, though it certainly can exist. I believe it is most often found to be a problem with people who have a history of drug and/or alcohol abuse/addiction - or, implicitly, are inclined towards such. As such, it's a rather personal question.
What do you mean by "convince your doc to to continue the prescription"? He already prescribed it to you, no? Why would he stop? Have there been warning signs of misuse or dependence? Also, are you getting therapy?