The frustration you are expressing is very common, since the lip moves so much it tends to crack and resplit frequently, making healing a slow process.
There are a few simple things you can do to speed healing. First, try to keep the lips well moisturized, typically with an antimicrobial ointment or something like vaseline. Keeping the air away from the healing cut will help the new skin cells grow in more quickly; also the thick greasy barrier will keep the new skin from drying out quickly, which should prevent splitting. Also, you will need to avoid picking at or otherwise manipulating the new healing tissue (for example do not try to remove any scab or peeling skin), as this will quickly lead to the area cracking back open again.
You should also check in about this issue with your primary care doctor
. They can take a look at the area and determine whether there is an infection or anything else delaying healing.
Also, if the cut is very deep, you should go to see your doctor right away regardless, as sometimes the deeper cuts require stitches in order to heal.