"... am ..."

[Odessa Dawn]

"I have been to Headley Court [the Forces’ rehabilitation centre] several times and am always struck by the people who have been injured who want to climb mountains, walk across the Arctic, have fresh adventures."
More: David Cameron: We must remember for ever, not just for today - Telegraph

Why was the nominative pronoun I dropped? Is it an optional?

[emsr2d2]

"I" was already used at the beginning of the sentence with "I have". Nothing has got in the way of that pronoun (no others have been used) so it is unnecessary to repeat "I".

I have been to Ireland and am convinced it is the most beautiful country in the world.
I have seen this film, thought it was great and want to see it again.
He gave me the bread, passed me the knife and told me to cut six slices.