If you were rejected only because you do not meet the criteria for common-law, then perhaps you might go and live with your sponsor for enough time to ensure you do qualify and appeal the decision so that you can show proof you do qualify. Or, if marriage is an option, then you might want to go ahead and get married and appeal the decision.
If you were rejected because they do not believe the relationship is bona-fide, then your appeal is much more complicated than just living together for enough time or getting married. You have to rebut any points made in the refusal letter concerning the genuineness of your relationship.