@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.
I have a subscription service with a local HVAC company. I have definitely use thema handful of times. I keep a list of electricians and plumbers and always ready to pay them extra to come out quickly. I have definitely had situations where I had to do that. The dishwasher broke once and I couldn’t get anybody fast enough so I gave the guests a free late check out and they were pretty happy. I also have multiple sets of dishes so all they were stuck with was a pile of dishes in the sink, not like they had to wash anything themselves. If washer and dryer broke, I would offer laundry service. Which has happened and guests did not take me up on it and ended up asking for a refund from ABB later. They never got one partially because it was all documented that I offered them The free laundry service.
@Dorothy179 we have been in this position-- most recently, as it happens, with a dishwasher.
@Sarah977 in our area, it is just very difficult to get any kind of emergency service, regardless of local relationships. In our recent case, after three days of trying and failing to get an "ASAP" service call we bought a floor model dishwasher from the closest (one-hour-distant) home goods store and our co-host installed it herself.
I agree with Sarah that the key in any such situation is transparency. Keep the guest informed about exactly what is happening and what the options are, and give them as much choice as possible at every point along the way.
If they choose to stay, whether to offer a refund and if so how much depends on what the amenity was and how long it was out. For water, or hot water, I'd offer a 100% refund for every day that it was out for more than 8 hours. If less than 8 hours, or for refrigerator/freezer, maybe 50%. For other appliances I would play it by ear depending on how inconvenienced the guest seemed to feel and frankly how much damage they are in a position to inflict with their review-- i.e., how new the listing is.