I heard from someone that if it takes way more than a month for your TA application to be approved it means that there might be some documents missing and you should contact your institution to make sure all your documents have been submitted
Please be informed that we are unable to provide you with an exact time-frame for the completion of the travel authorization application process. Kindly note that there are multiple levels of processing involved to approve the travel request by students. The decision to issue the travel approval letter is solely at the discretion of the Immigration Department. Rest assured that, your institution will be notified of the progress of your application.