Lips get loose and fatigued

Hi! I just got a C* alto sax mouthpiece a couple months ago and since my past 4 weeks my lips have been getting fatigued real easily. I have a good tone and everything, it's just that I have a very weak endurance and just playing for a minute will start to make my embouchure tighten up and just give up. Before I had a problem that my lips and mouth muscles were hurting, but not they're just getting tired easily. Do I have to get used to the C* mouthpiece still or should I look for other mouthpieces? 

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