@Dorothy179 Well, first of all, maybe you could try to establish some sort of relationship with a local appliance repair, let them know about your Airbnb business, and that time would be of the essence. In areas where I have lived, there were always one or two guys who had small business appliance repairs- those might be better to look for than some big company. In other words, try to find "your" guy, who will be willing to come to the rescue asap.
A dishwasher breaking down isn't as crucial as a fridge or a hot water heater, as dishes can always be washed by hand.
For fridge breakdown prep, keep a couple of coolers handy- ice could be bought and guests can store their food in those if need be.
Of course, if something goes on the blink just before a guest is due to come, you should let them know immediately, along with what you have in place to mitigate the inconvenience in the meantime, and when it might be able to get repaired. If it's a deal-breaker for them, I would just refund them. If they indicate they want to come anyway, just let them know you can't guarantee exactly when it will be fixed, but of course you'll do your best to rush it, and for something major, you should offer a discount. I'm not good at coming up with suitable percentages for that, hopefully other hosts here will say what they think it warrants.
Some guests are quite adaptable and don't get their knickers in a knot about things, others may show a lot of irritation.
Resist the urge to apologize profusely, as if you did something wrong- s**t happens, you try to be accommmodating and deal with getting it repaired. If you act mortified, those really irritated types may take advantage of that to stay, and then demand a full refund afterwards, which you definitely want to avoid.
If something just goes on the blink briefly, like say the guests are without hot water for an hour because you find it was just a tripped breaker, that's not something you have to right away offer to throw the guest a discount for- apologize for inconvenience (a tripped breaker is often the guest's fault- i.e. they had far too many things plugged into the same circuit) and maybe bring them something nice from the bakery, or a bottle of wine if you can see that they indulge in that, by way of apology.