First of all, as I understand it, timeouts should not come into play for services that are down. There should be a much quicker response from the endpoint in that use case. Timeouts typically are for services that take a long time to respond.
Secondly, if you always want to insure customer just continues browsing, you can queue the request and Pega will have an Agent make the asynchronous call. When the service is down, the processor (invoked by agent when queued items are picked up) will make the number of attempts you specify and then move the item to the Broken-Queue. Using this approach, you can also configure a synchronous response at a later time by providing the user with the "queued item id" and providing the functionality for them to "get results".