Absolutely worth a shot. It takes a lot more effort to provide and exercise supervised visitation. No point in dragging the child down there to be repeatedly disappointed if the other parent doesn't care enough to show up. Get an experienced family law attorney to do this for you.
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.
Mr. Moore is absolutely correct. If the child's parent cannot make supervised visits, now would be a good time to try and get more flexibility for you and your child.
I am licensed to practice law in the great state of Texas only. The above answer does not create an attorney/client relationship. These responses should be considered general legal education and are intended to provide general information about the question asked. Frequently, the question does not include important facts that, if known, could significantly change the answer. Information provided on this site should not be used as a substitute for competent legal advice from a licensed attorney that practices in your state. The law changes frequently and varies from state to state. You should verify and confirm any information provided with an attorney licensed in your state.
A judge would certainly look at the pattern of missed and late visits. You should speak to a good family lawyer about this right away.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.