If one of my suppliers goes down, can my customers still search and book on my website?

Yes, in most cases your website keeps working, because each supplier is connected separately and a search goes out to all of them at the same time.

When one supplier stops replying, the search returns the results from the suppliers that did reply, and your customer sees fewer options instead of an error page. A hotel search that normally pulls from three sources will still show what the other two sent back. Booking works the same way, as long as the option your customer picked came from a supplier that is still responding.

Where this does hurt you is when the supplier that is down is the only one you have connected for that product, or for that part of the world. If you have a single flight source and it goes quiet, flight search has nothing to fall back on, and all you can do is wait for them to come back. It also matters if the outage lands between the moment a booking is sent and the moment the confirmation comes back, because then the booking has to be checked directly with the supplier before you tell your customer anything. Some suppliers send a clear failure message, others simply stop answering, so the picture is not always as tidy as you would like.

Check how many live sources you have for each product you sell, and if any of them is the only source for something, ask about adding a second supplier for that same product.