The reason you are experiencing this issue is because 'abandoned' is not a valid value for an order's financial status.
The documentation clearly states that the financial_status could be set to abandoned.
http://docs.shopify.com/api/order
According to the linked documentation, financial_status can be set to one of the following statuses:
- pending
- authorized
- partially_paid
- paid
- partially_refunded
- refunded
- voided
This does not include 'abandoned'.
Why not just get the whole list back by hitting the checkout API, and then filter through them based on customer ID on the app-side?
Right now your posts kind of read along the lines of:
I'm using Shopify's API in a manner that they did not intend for it to be used, and I'm unable to achieve my desired outcome. Could this possibly be a bug on Shopify's end?