Caching on the client side is going to be very important for a lot of well performing Hypermedia clients. Here is some more specific guidance straight from Fielding's dissertation:
The advantage of adding cache constraints is that they have the potential to partially or completely eliminate some interactions, improving efficiency, scalability, and user-perceived performance by reducing the average latency of a series of interactions. The trade-off, however, is that a cache can decrease reliability if stale data within the cache differs significantly from the data that would have been obtained had the request been sent directly to the server.
The are trade offs but event a short time frame for caching will greatly improve performance. Ideally the Hypermedia API will provide caching guidance. This could be done in the same manner that HTML caching works with the browser and Expires and Cache-Control headers.
Also if the resource has moved then the API should inform you with the proper 301 Moved Permanently response.