You are my constant reminder that promises are made to be broken.
This is correct. Promises are made to be broken is a common axiom in English. This sentence says the behavior of you constantly reminds the speaker of the truth of the maxim. Presumably you frequently makes and breaks promises.
You are my constant reminder that the promises are made to be broken.
Adding the makes promises refer to some specific set of promises made by you to the speaker. This phrasing sounds odd because promises are made is a strange conjugation in this case. Are made refers to a current, ongoing act of creation which lasts over a significant amount of time. Making a promise is a single, simple action. If there's a specific set of promises (whether broken or not), then they were made in the past, are being made right now, or will be made in the future. Technically, this is correct, but it's extremely unusual, because people don't continually make the same promise over a long period of time.
Use the first statement. Without the, promises refers to all promises, and it's fair to say that promises in general continue to be made. Either way (with or without the article), those involved in the conversation will understand from the context which promises exactly were broken.