So under the current RoA set up, you can activate one free artefact per day. On a 1x server this lasts 24hrs. This means that 24hrs after you activated your diet (for e.g.) you would need to manually re-activate it 24hrs later. If your account is pretty active, then a few minutes of cross over isn't the end of the world. But if we had the option to automatically renew an artefact, that could make it easier to avoid sudden loss of key artefacts. If players wanted to automatically renew more than 1, it would charge them 5 / 10 gold from their gold pool every day until manually removed.
It could work the same as renewing plus or wheat bonuses, so if a player is trying to renew two artefacts and they're out of gold then it won't renew one of them. If TG want to be really smart, they could put timestamps on the renewals so that the first one chosen for auto-renew gets renewed regardless of a players gold pool as it's the free one per day, and the latter chosen artefact doesn't get renewed.