The word "most inconstantly" refers to something that occurs with varying frequency or unreliability. Some synonyms that can be used to describe this term include inconsistently, erratically, irregularly, intermittently, sporadically, fitfully, haphazardly, and unpredictably. These words all convey the idea that the occurrence is not consistent, and may happen frequently or infrequently, without a set pattern or schedule. Whether used in conversation or writing, understanding these synonyms can help to convey a more precise meaning, and allow the speaker or writer to match the word to the specific context or need.