If one of my suppliers goes down, will my whole website stop working or will it still show the other suppliers?

Yes, if one supplier goes offline your website normally keeps working and shows the results that came back from your other suppliers. When a customer searches, the request goes out to every supplier you have switched on, and each one answers on its own. If one of them does not answer in time, or answers with an error, that supplier is simply left out of the list and the rest of the results are shown as usual.

There are limits worth knowing. If the supplier that is down is the only one you have connected for that product, the search will come back empty and there is nothing the system can put in its place. A supplier can also be slow rather than fully down, and then the search takes longer before their results are dropped. Whether you get any warning of an outage depends on the supplier, as some announce planned maintenance and others do not.

Bookings are different from searches. If a supplier is down while your customer is paying, that booking cannot be completed until they are back, and the same is true for a cancellation or an amendment on a booking that was made with them. The bookings you already hold are not lost, they simply cannot be changed until the connection is working again.

The most useful thing you can do is check how many live suppliers you have for each product you sell, so that no part of your website rests on a single connection, and ask your support contact to tell you when a supplier is taken offline for maintenance.