We are doing this on a daily basis and we haven't had any issues with accessing the backend of Sitefinity from another computer. My suggestion is to try to explicitly hit the backend entry page e.g. http://servername/Sitefinity and log in, then check whether the problem persists.
Please let us know whether your issue is resolved, and do not hesitate to contact us again.
All the best,
the Telerik team
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