Reusing reference letters
Reusing a reference letter is not itself a problem, but good reference letters are tailored for the target goal.
A letter writer is likely to reuse substantial portions of a letter for the same candidate without you asking.
I think the warning about time is more likely to be encouraging you to give a substantial time cushion or alternatively to make sure you have a backup if he has to say no, not meant to dissuade you from asking again.
When you ask, remind and thank the writer for the past letters. You don't need to ask that they reuse one, they can manage that on their own.