"Abstain from all observance of Sabbaths" (St. Cyril of Jerusalem - Cat. 4:37) is a sentiment shared by most of the Fathers as far as I am aware.
To observe the Sabbath as a custom - rather than a Law of God necessary for salvation - seems acceptable. Much in the same way that getting circumcised or keeping kosher for cultural reasons would be. From previous discussions on the board, I'm not sure which category Ethiopian Sabbath observance falls into.
In liturgical books, major feast days are often marked with the words "Rest from work." Therefore it would seen that the purpose of Christian Sabbath observance - if it can be so-called - is to allow a person to focus on the feast. In a normal week, the day of Resurrection seems to be the most appropriate day for such an intensified focus on prayer. That being said, total fasting is prohibited, and prostrations normally not performed on Saturdays in honour of the Sabbath.
I'm still confused as to what extent the 7th day should be honoured above the other days of the week, but strict Sabbath observance as performed by the Jews seems to be almost universally condemned by the Fathers, and a relatively late decision of the Tewahido Church.