Is it possible for a bruise to never go away? my 2 year old got a black eye 1 month ago and there is still bruising around her eye.

Not likely.: U -r most likely referring to a residual darkness and not an actual bruise. What most likely is happening is that the " initial bruise" that he suffered stained his skin due to the deposit of heme , its what gives blood its color. Normally the bruise goes through color changes but a small amount of staining is not unusual in the delicate tissues around the eye. It may take some time fade.

It might be pigment: Sometimes after a bruise there is residual pigmentation (hemosiderin and/or melanin) that is left after the blood itself is cleared away. This can take months to fully clear for some people. It is very unlikely that this will persist much longer than a few months, so if it is not clearing or if it seems to be worsening, i'd recommend seeing your doctor.

Never can be long!: For "black eyes' to go away, blood first breaks down, and then absorbed. If there was a lot of blood, it depends on whether it damaged blood vessels that must first grow back before anything can be absorbed) and if there was severe injury to other structures. It could take months. If she has "easy bruising", other conditions may be present & require further testing to find hidden diseases.