Maintaining a single instance to a RestSharp client

Whenever in doubt and if possible, look at the source code.

From a brief look it seems acceptable and even the better approach to hold on to a single instance, as it mainly responsible for executing IRestRequest requests.

I was once in doubt with the same question regarding HttpClient and found the following:

The default HttpClient is the simplest way in which you can start sending requests. A single HttpClient can be used to send as many HTTP requests as you want concurrently so in many scenarios you can just create one HttpClient and then use that for all your requests.

If concurrency is required, explore the source code to see if there may be any pitfalls. You can always default back to HttpClient which is a part of the BCL since .NET 4.5 (and can be installed via NuGet on .NET 4.0)