You posted on the Beta Connector thread but regardless of whether you're using the Beta Connector or not, your issue is related to Google rate-limiting you. It seems that your document has over 1800 citations (wow!) and Zotero Connector can only update them 32 at a time, so a single full-update to your document takes over 50 (heavy-weight) transactions to Google servers. Google doesn't like that and if you were updating your document multiple times Google may have decided to temporarily limit you from doing this.
We don't really recommend working with documents of this size in Google Docs in general, it is not very well suited for big documents and even their own editor slows down significantly with big docs. Moreover, you run into problems like this. Since you've already done this, your best bet is to stop trying to update your document with Zotero for a while and try again later. If you're not close to being done with this paper, you may want to move your document with Zotero citations to a different word processor.
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I couldn't add citations to Google Doc
We don't really recommend working with documents of this size in Google Docs in general, it is not very well suited for big documents and even their own editor slows down significantly with big docs. Moreover, you run into problems like this. Since you've already done this, your best bet is to stop trying to update your document with Zotero for a while and try again later. If you're not close to being done with this paper, you may want to move your document with Zotero citations to a different word processor.