You ask a very important question and one that does not have a one size fits all answer.
Several pieces of information would be important in coming to an answer.
The short doctor name for an enlarged prostate is BPH. This stands for benign prostatic hyperplasia.
Have you taken the BPH questionnaire? It asks seven questions about your urinary function, and a quality of life question. It helps inform your doctor about how much BPH symptoms bother you personally.
If you havent done so already, ask your doctor for one. Fill it out and see how you are doing now, while you are still taking the medications.
Its also important to determine the amount of urine you have left in your bladder after emptying your bladder. Its a simple test -- called the post void residual -- done with an ultrasound machine in the doctors office. This result, along with the results of your questionnaire, would be important factors in deciding if and when to stop taking one or both medications.
A third important aspect is what, if any, side effects you have from your medications. Some patients have few and others have significant ones, including sexual dysfunction.
Its common for patients to go off of these treatments and see how they do. If the symptoms come back, then they will go back on them. Some men are on medicine for BPH for many years. Other men cant tolerate the side effects and choose other treatments, such as surgery. And other men can get along without any medicine after the initial prostate shrinkage has taken place. So theres no one answer for your important question.
One other thing: One group of men who need their PSA checked are those who take finasteride. The baseline PSA before finasteride should be measured. And then at 6 months, if the PSA value does not go down by at least 50% from baseline, you may want to speak to a urologist. This may be a sign of prostate cancer.