It sounds like you may be sending your requests too quickly - the API call limit allows 40 calls overall, but it will also restrict you to 2 calls per second. If you were to space your calls out a bit more, this shouldn't be an issue.
These are some requests which received 429 error and receiving time
09bfad82-e3ff-4228-a746-a73f8c10f399 2017-10-05 22:31:34,363 a9cd3567-c843-4a08-931e-da5a3a77be84 2017-10-05 22:31:36,353 01b24e93-98bd-4754-9f98-c775fd60724c 2017-10-05 22:31:38,358 32ca2688-3c34-4719-ac20-979ef3342571 2017-10-05 22:31:46,235 9447abc0-7f33-4ce8-ba28-3a890c6ae15a 2017-10-05 22:31:48,252 749f8215-be1d-48ca-bfb7-661f5143d5e4 2017-10-05 22:31:50,244
Well it certainly did turn out to be interesting, it looks like affiliate shops have a different throttle limit for creating a few specific resources like fulfillments. And it's 5 calls as you mentioned earlier.
What I'm not 100% sure of as of yet is if the leak rate is the same as paid shops are before you're able to make calls again. Have you tried to delay your calls by anything more than 0.5 seconds in between?
Some additional information to pass along - currently on affiliate or trial shops the throttle limit is 5 per minute on certain actions. This is newer functionality, so we're going to look into documenting this more clearly.
If you were to sign the shop up for a paid plan, the throttle will increase to its normal levels again.
Why is this still not documented?!
It toke me 2 days of work to figure the API error was because this "SECRET" throttlelling.
This information should be clearly documented in: https://help.shopify.com/api/getting-started/api-call-limit
Guille - it may not have been spotted but it is documented on the fulfilment api docs:
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