The error message was introduced in Resilio Connect 3.8.0 together with implemented integration with Sharepoint Online.
To optimize performance, Sharepoint itself throttles the requests made by an application, so as not to exceed the defined usage limits. Read more about it here.
Resilio Connect Agent is also affected as it works with Sharepoint Online through an application. The above mentioned usage quotas are not limited only to the files uploaded to Sharepoint. The quotas include basically every request made by the Agent, such as request to list the available sites, to run test connection, perform periodic scan, read and write some metadata on files, etc.
However, it's true that the more files are synced, the faster the quotas are consumed. As a result, some requests to Sharepoint may temporarily fail or work slower, overall speed of synchronization may be low.
The error message is an indicator that the Resilio Agent is throttled at the moment. It does not mean that the Agent is underperforming or does not work. Once the daily or minute quotas are reset, the Agent will continue the work at fastest available pace.
The error message is reset automatically in 5 minutes, and appears again when the Agent is throttled again.
Additionally, symptoms and consequences of the throttling may be observed in other functionality in the job, for example, browsing through Sharepoint's sites, real-time updating of active files download queue and/or job events.
How to fix it
On the Resilio Connect side it's only possible to apply the Preset for Sharepoint in the Agent Profile. It's optimized for most usecases. You might want to contact Resilio Support Team to try and optimize it more for your specific usecase.
The rest is beyond Resilio control and must be addressed on the Sharepoint side.
Error code SE_FS_CLOUD_AGENT_BEING_THROTTLED