Although not all cases of brown vaginal discharge
are cause for concern but in your case there is definitely a cause for concern as it has been going for past more than a month.
Normally brown vaginal discharge is most often associated with old endometrial cells but it can also be a symptom of a medical concern that is much more sinister than leftover endometrial cells.
Some common conditions causing brown vaginal discharge include
Pelvic Inflammatory Disease
Sexually transmitted diseases like gonorrhea, Chlamydia or vaginal warts.
Although each of the above mentioned have much more noticeable symptoms in addition to brown discharge like pain,burning,itching,pain during intercourse
,vaginal dryness,loss of appetite etc.
What you require is a thorough examination by a Gynecologist and determining the cause.
Treatment can be suitably instituted once the cause is identified.