The simple answer is that it shouldn't affect things. The registrar is responsible for handing the Root servers their portion of the delegated domains. If the registrar goes down, the Root servers will use the data from the last received update.
Changes that you make that haven't been submitted to the Root Servers may not be published.
Once connectivity is reestablished, they will submit their updates.
As a side note, Network Solutions is starting root zone updates twice a day which will make nameserver changes go a little more quickly. Not a big deal if you're not moving your site from one nameserver to another, but, a welcome change.
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