可以省略。

一般说来，在并列连词（如and, but, or等）之后，可以省略与前面分句重复的主语和表语。你这个句子可以改为：

He is faced with many difficulties, but capable to overcome them. 

又如：

Some animals are awkward on land but able to move easily in the water. 有些动物在陆地上很笨,但在水里能活动自如。

The game is very delicate, but able to make people tired of playing on the day! 这个游戏非常精致,但是却能让人不厌其烦的玩上一天!

I was imediately revived and able to give my speech. 我立刻恢复了精神，能够发表演讲了。

He was bankrupt and unable to pay his debts. 他破产了，不能偿还自己的债务。