The Hue Bridge limits how many requests it will process during a certain time. Exactly how many and during what time window is unknown, but it seems like it may be around 10 requests per second.
When the rate limit is hit, the bridge responds with HTTP status error code 429 and the message "Too Many Requests", and no data is returned in the response.
Note that the rate limit is not per application. If you have many different applications running (on your phone, your laptop, a Raspberry Pi, etc) they all contribute to reaching the rate limit.
The error is temporary, so it will solve itself if you wait a while (15 minutes or so, to be sure). If it happens frequently you may consider what applications you have running at the same time, and either remove or temporarily disable some of them.