Are Sensei by there title and ability unbeatable?

No, fighting proficiency is not necessarily the criteria one should use to determine if the person is deserving of the title Sensei and the position in the dojo of Sensei. The proficiency in fighting and sparring is only a very small part of being a Sensei. I look at Sensei more as a mentor, one who has the experience in the system and holds within the shu-ha-ri principle of it. They are able to impart the physical, mental and spiritual aspects as well as the essence of the system.

It is almost always up to the individual to develop skills and if you are able to defeat Sensei, all the better but don't let that singular victory defeat your efforts to seek out more and more and more of the entire, holistic and wholehearted system we call karate goshin-jutsu-do.

I was able to thump on my Sensei in 79 on Okinawa but he still had plenty to teach me and I listened as I still listen to his advice and guidance today.

p.s. by the way, the next night he let me have it good so you can say we floated back and forth as to who got the best of who in kumite. :-)