Translation:I have been accustomed to that for a long time.
Because this is something that started in the past and continues into the present. Other examples:
(edit: on further reflection this is a bit more complicated, see the other comments)
Actually contrary to my previous comment I agree with you and MarkWootton for the preferred translation which is "I have been accustomed to that for a long time."
Another accepted answer (which is the one I entered) is 'I have been getting used to that for a long time', and I feel '-as' works better for that than '-is'.
"Mi delonge kutimiĝas al tio." Or "Mi delonge alkutimiĝas tion."
But not: "Mi delonge alkutimiĝas al tio."
If you put the "al" as an affix, the whole idea is that it replaces the preposition without an affix. Well, I think so, for the grammar of the sentence.
However, this precise item is for auditive comprehension and the person distinctly said the above-noted sentence.