I've been trying to use the backup service but it has not been going.

Moses, It could be that the system is having temporal issue which require that you can try it again in next few hours.
There are 2 ways you can access backup, you can access your backup contacts via the SIM Toolkit on your phone or via the backup portal.

To retrieve your backed up SIM contacts via SIM Toolkit Service, Go to the menu on your phone>select MTN services>MTN Backup>Backup SIM contacts>it will prompt you to synchronise your SIM contacts>press Yes or OK> then the synchronisation starts, provided you have up to N50 in your account. Then power off and power on your phone.

You can access or restore your MTN Back-Up details through the self-care interface via https://mtnnigeria.weballynis.gemalto.com/CloudBackup/ind... then, you will need to login using the information received by SMS.
If you did not receive an SMS with your login and password, you can get access through the Self-Care interface by:
a. Clicking on “Do not have an account yet” if you have never received the access information before
b. Clicking on “Forgot your Password” if you received it and then forgot it