Q. Why is it that on Sundays you can do whatever you gave up for lent?
A. Ah, yes, this is one of those things that many people do not realize. I think the answer could be given in two different ways. There is no clear teaching on this since giving something up in Lent is more of a personal sacrifice even though it is encouraged as a Church discipline. Let me share the two approaches you could take.
First of all, there are those who prefer to give something up all of Lent. That means from Ash Wednesday through Holy Saturday and every day in between. This is certainly a good practice and one that will bring with it much merit. The rational would be that Jesus fasted in the desert for forty days and did not have any breaks or moments of feasting. Additionally, as a Church we do have a penitential attitude even toward Sundays in Lent in that we keep the Church decorated in a very simple way, wear purple as a sign of penance, and refrain from singing the Gloria and the Alleluia. These are all ways we keep the attitude of penance even on Sundays.
However, with that said, it's also important to point out that Sundays are Solemnities within the Church. A Solemnity is a day of the greatest celebration and especially focuses upon the entire action of Christ's life, death AND resurrection. So Sundays are not technically to be days of fast; rather, they are to be days of feasting!
As a child I remember approaching Lent in this way and have always continued this practice. For me, it has always been a welcome moment of rest from the penance of Lent and has helped me remember that the joy of Easter is the final goal of any fasting and penance. Psychologically and spiritually it seems good to celebrate these mini-celebrations of Easter every Sunday and it seems to help make the days of fast more meaningful. It adds a certain rhythm to the week focusing on both celebration and penance at the appropriate times.
Additionally, there are two other solemnities within Lent that some will choose to treat as a Sunday. The Solemnity of St. Joseph is on March 19th and the Solemnity of the Annunciation is on March 25 (nine months before Christmas marking the Incarnation). These days, being Solemnities within our Church, are celebrated with the same joy as Sunday. Therefore, it would be understandable if you decided to give up your Lenten sacrifice on those days also.
The bottom line is that sacrifice and penance is for a purpose. It's a means to an end, not an end in itself. In other words, our ultimate goal is not sacrifice and penance; rather, our ultimate goal is the resurrection. Penance helps us on that journey but penance should never be seen as the final end.
So my recommendation is to celebrate and to celebrate all Solemnities within our Church well. This will only help make the days of penance more fruitful.