Concurrent connections
What actually gets counted, and why it is not your request count.
One "concurrent connection" is one connection that is currently open. Think of supermarket tills: however long the queue, only as many people are served at once as there are tills.
What counts, and what does not
What counts is connections open at the same moment — not your daily request count. A tool that pulls 200 pages one after another uses 1 connection. A tool that pulls 200 pages at once uses 200.
The limit
5,000 per account. Past that, the next request is refused until one finishes. Your GB quota is not debited when that happens — the queue is simply full for a moment.
How to fix it
Lower the concurrency setting in your tool. It is usually called "threads", "concurrency", or "connections". Lower it, retry, then raise it slowly until you find a level that holds.