Any limits placed on sending and receiving invoices is based on the accounting package you have chosen.
Not all accounting packages enforce limits and the limits vary from package to package.
Generally the limits will not affect small to medium business and are only applicable to businesses with very high transaction volumes. You will need to research your chosen software's documented system limits.
Billx has taken ever measure to reduce the API calls so that you will not experience any excessive usage limit. If you can generate the invoice in your accounting software, then Billx will more than likely be able to deliver the record to your customer.
Billx does not enforce any limits to the number of invoices you can send and receive via Billx.