I consider myself to have above average knowledge on the topic of penance, since I have spent a lot of time researching and writing about the topic. But, after just typing that attention-grabbing title above, I will now humbly admit that I do not profess to be giving "the definitive answer on observing Lenten resolutions on Sunday." That is because the changes to penance made by the National Catholic Conference of Bishops in November of 1966 have dramatically altered the way Lenten penance is practiced in the United States, by fracturing or diversifying penance and basically assigning responsibility for the Lenten resolution to the individual. This fact makes it difficult to provide an absolute answer as to observing Lenten resolutions on a Sunday.
The last Lent prior to the changes in the U.S. found Catholics fasting every day of Lent. This Catholic fast is characterized by one full meal and two smaller meals (or "collations") that do not total one full meal. Generally in the Catholic Church, Catholics abstain from meat during the season of Lent. In the United States, the so called "workingman's indult" had been extended to all the faithful, allowing for them to have meat at their principal meal (the one full meal). The change that allowed the faithful to choose their own Lenten penance reduced these fast days to two: Ash Wednesday and Good Friday, and it replaced the Lenten fast with the direction to choose one's own Lenten resolution.
The great variety of Lenten resolutions make it difficult to provide one definitive answer as to observing a Lenten resolution on Sundays. One could argue that it is better to observe the resolution on Sundays so as not to kill the momentum of the sacrifice. We form habits with our resolutions, habits that might be imperiled when we take a day off. People also argue that these are Sundays "of Lent," and that it is somehow lazy to take a day off from our Lenten penance. Jesus fasted for forty days in the desert; he didn't have a feast every seven days. Then there is always the possibility that someone might have a resolution focused on Sundays, such as visiting the elderly on Sunday afternoons. Obviously they wouldn't want to exempt themselves from this Lenten resolution on Sundays, since this is the day they have chosen to do it. So also if they have added an extra prayer they intend to do on Sundays, since as saying a Rosary.
On the other hand, Sundays are NOT counted within the forty days of Lent. This means that, technically speaking, Sunday can be a day of rest from the Lenten resolution. Of course, if you give up beer for Lent, you shouldn't use Sunday as an excuse to drink a six-pack. If you give up chocolate for Lent, you shouldn't indulge by eating a whole bag of Lindt truffles. But Sunday is a day to rejoice in the Lord, and though they are Sundays "of Lent," they are particular days to anticipate the upcoming Easter celebration. So there is nothing wrong with taking a break from a Lenten resolution on a Sunday. In fact, doing so can be a powerful reminder that Lent is not simply about our individual will-power and heroic virtue, but about the gift of God in the paschal mystery - the life, death, and resurrection of Jesus. The victory is already won for us, but it is not won through us, but rather through Jesus.
So there you have the definitive answer on observing Lenten resolutions. It's your choice. You shouldn't feel obligated to maintain your Lenten penance on a Sunday, and this means you should make the decision based on what you think will help you to grow closer to God and prepare best for Easter. That is the purpose of Lent, after all. Rather than spend too much time debating, deliberating, or discerning, you might instead think about how you can better observe Sunday as the Lord's Day.