This is less of a whine and more of a request for advice. I have a very difficult time understanding people with heavy accents — not people from English-speaking countries, but people from, say India or China. I work with several and while I concentrate on their words, I can usually only understand about a third of what they say. I hate to ask them to repeat what they said, but sometimes I have to — and often don’t understand that either.
What should I do and how many times is it appropriate to ask them to repeat themselves?
Cedar Waxwing's 365 
Well, I suppose you could be like my husband who just nods in agreement even when he has no idea what he’s agreeing to. (I think I have found my next complaint).
Uh-oh, be careful he doesn’t get roped into wearing a puffy shirt.
Sister-Dona. Yes, we intersect again. I am hopeless with certain accents…basically all the ones that involve a more musical approach to the language, so sometimes even the Irish leave me in the dark. I’ve pissed off many a fine English-speaking person because I simply cannot hear the words through the fog of the accent.
I also have to listen very carefully. My former parish was an immigrant center, mostly from southeast Asia and East Africa, and I found myself leaning in further and further in conversation to try to parse out the words.
Ooh, tough one. I generally ask people to repeat themselves once, and if I still don’t understand, I resort to Sabine’s husband’s strategy.
Okay, you guys all realise you are the ones with the accents, right? lol
How many times you ask them to repeat themselves depends on how much you need to know exactly what they are saying. After asking them once or twice to repeat it, can you just say, “I’m sorry, I’m having trouble with your accent. This is what I think you’re saying? …”
Now that you say that, Linda, I have done that when I really needed to know what was said, then followed it up with an email.