I think Dibdin - at least the songs I know - are fairly representative of his time period. The words are dated and I think that accounts for the lack of popularity. After all, one can't, in today's day and age, talk of "His form was of the manliest beauty, His heart was kind and soft. Faithful, below, he did his duty," etc. as one used to. The songs speak of the common sailor with affection and admiration. It's easy for me to see why they were popular then. And I think they are worth a listen if only for that reason. (This from a historian not a musician!)

As to enduring - well there are a lot of folksongs that have endured that I don't like as much as I like Tom Bowling!