Damage to which portion of the limbic system results in loss of memory of recent events and difficulty committing anything new to memory?

Hippocampus.

Explanation:

There are two parts of the limbic system. They are the frontal part which is the amygdala and the posterior part which is the hippocampus.

The hippocampus is an extension of the temporal part  of the cerebral cortex which is a plastic-like structure that can be easily damaged by stimuli. It is packed with densed neurons and forms an S-shape at the extension of the temporal part.

It is responsible for learning and memory and damage to it can result to memory loss of recently learnt information.