Frank Illing shares his Maya Batch Render Region script BatchRenderRegion.mel which will allow you to render animated regions inside the Maya Render View window. Check out Batch Render Region for Maya here.

BatchRenderRegion.mel is a rendering utility that lets you correct little errors in image sequences without the need to rerender whole frames or using an compositing software and messing around with mask setups etc.

With it you can define render regions in a sort of setting key regions over time and then let the tool interpolate between them during batch rendering sequences inside the render view window. Also one can use a built in object tracker to get the regions of certain types of objects inside the render view automatically.

It loads images of sequences according to their frame numbers into the render view and replaces their faulty image regions with the new rendered region. It also has the support for external batch renderers including a built in composer to merge the external rendered regions with existing image sequences.