I've personally always struggled with understanding people. I don't have a hearing problem, but I do have issue parsing the sound that I hear (even in my own native language).
I'm well aware of the awkwardness that entails having to ask someone to repeat the same thing several times. They are likely to get annoyed, feeling that you're the problem.
The easiest way to avoid the problem (= the person getting upset at your ineptitude) is by pointing at your ineptitude yourself. In principle, it's the same as making jokes about yourself so that others are less inclined to do so at your expense.
1. Put the blame on yourself.
I'm not suggesting that you've been explicitly blaming the American for speaking fast, but the way you address the problem can cause such an inference.
Can you please talk more slowly?
You're being efficient by asking the easiest fix for the current problem (that you can't understand them). Consider the more polite alternative:
I'm sorry, my English isn't as good. Would you mind speaking more slowly?
This puts the blame on yourself. Because of that, asking them to speak slowly clearly means that you're asking them a favor, rather than trying to imply that they are responsible for speaking too fast.
Indirectly, this also reminds them that you are doing your best to speak to them in their native language, which is not your native language. That reminder may make them more understanding of any communication issues that arise.
2. Point out the cause once. Experience the problem repeatedly.
After you've asked them to speak more slowly, don't repeat that question. Repeating it insinuates that they didn't listen to your earlier request.
You can get away with asking them to speak even slower, but you can only really do that once, and the problem may occur again.
Instead, don't point out the problem anymore. Just ask them to repeat themselves.
American gdajlgjagllmalvmlagjagmalvmalmldmamglanvammeao
You I'm sorry, my English isn't as good as yours. Would you mind speaking more slowly?
American I would like to jagmalvmalmldmamglanvammeao
You I'm sorry, could you repeat that?
American I would like to book a table.
You What date would you like to make a reservation for?
American vmalmldmamglanvammeao
You I'm sorry, could you repeat that?
You pointed out the problem (fast speaking) once. Don't keep bringing attention to it, because that can be inferred as pointing out that they ignored your request.
However, since you honestly did not understand them, it's fair that you ask them to repeat themselves. The alternative (guessing what they said) would be much more impolite.
If you feel that they are getting annoyed by your requests for them to repeat themselves, apologize for being the cause of the issue. To the American, you are indeed the cause of the issue; he's used to being understood when he speaks the way that he does.
3. Prove that you're making an effort.
Notice the difference between the two responses:
1
American Excuse me, I was told that pgofdfdofz would be available today.
You I'm sorry, I didn't catch that. Could you please repeat that?
American I was told that the jacuzzi would be available today.
2
American Excuse me, I was told that pgofdfdofz would be available today.
You I'm sorry, I didn't catch that. What is supposed to be available today?
American The jacuzzi.
In the second example, you are proving that you understood most of what they said, but you didn't catch one important part. By asking what that specific part is, you are implicitly confirming that you understood everything else.
This also means that the American might only repeat the words that you missed, which may be easier for you to understand, compared to hearing the entire sentence again.
There's no way to guarantee that the person will not be upset. However, there are different reasons as to why the person may become upset, and you can try to minimize the reasons.
- By expressing that your English is not good, you are reassuring the person that they are not at fault here. If they feel at fault, they will become defensive, which can manifest itself as getting upset.
- If they feel that the problem is caused by your (by not paying attention properly), they may get upset with you. By repeating what you did understand, you are proving to them that you're actually making an effort.
However, if they get upset because it's annoying to have to repeat themselves, then there is little you can do to prevent them from getting upset. If you didn't understand what they said, the only option you have is to ask them to repeat themselves. If they refuse to do so, then there's not much you can do about that other than apologize.