It sounds like you are using strip wax?
If the wax is not coming off you would need to put more wax over the top, press your strip in, get a good grip of the strip as close to the waxed area as possible, make sure you are pulling the skin as tight as possible with your other hand and make sure your client is pulling her skin tight as well - remove the strip with power, making sure you pull the strip back on itself and not upwards.
For this treatment, cut the strip in half lengthways as this will allow you more control and precision and less hair breakage.
If you are using hot wax you would still apply more wax and use pretty much the same technique as above but use the normal hot wax process to remove.