Just an FYI. I flew in with my 4 piece fly rod in my backpack in a rod tube. On the outbound flight from Roatan security would not let me take it on, had to go back to the counter and check it. I discussed this with the head of security and he went and got the regulation book showing me that indeed fishing rods are prohibited. Strangely enough the person in the seat next to me was able to carry on his rods.
Seems like a bit of a crap shoot. I would advise that you bring a rod tube that will fit in your checked luggage. It can be a little but hectic flying out on one of the Saturday flights.