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Jean, very strange this behavior. You are hosting your WEBAPI on a website?
If yes, validate if it is in free mode (it may be a problem). However, even in free mode, you should get more answers.
What I imagine is happening. Your WEBAPI goes a while without receiving requests and IIS puts your site (api) on standby. In the next Request, IIS moves up the site again, but for some reason, your API client must be on a low timeout.
Set Always on mode and see if it solves your problem:
Jean, you can send the Webapi code, because the one you posted is from the client consuming the API, right? It will certainly help us to help you. :)
– Thiago Lunardi