Hand fatigue when playing certain things on guitar. How do I get rid of this?

I can practice for an hour and not feel anything in my left hand, but
as soon as start playing certain chord progressions or patterns my
left hand gives out. For example, when I play "Snow" by Red Hot Chili
Peppers my hand starts hurting within a minute. Why is this? Am I
doing something wrong? Should I push myself and try to increase my
hand's stamina?