Add the tomatoes, onion and peppers to a medium-sized sauce pot.
Sprinkle with the sugar and drizzle with the lime juice. Mix well and turn the heat to high.
Bring to a boil and then immediately turn the heat to low and let it simmer gently until it's nicely thickened, about 2 hours.
Let the preserves cool completely before refrigerating. (Wrapped tightly, this will keep in the refrigerator for about 3 weeks.)