To condition arms i would start shadow boxing with the same weight gloves you spar with. It will get you used to missing shots and hitting air which is when your arms start getting tired. Or if your the overachiever shadow box with 2 or 5 lbs dumbbells or weighted wrist wraps. Than do exercises to train the lats. Your lats play a roll in retracting your arm quickly so it doesn't hang making it more tired. Try pullups or just look up exercises online for lats that's well suited to you. On the heavy bag do one round of just speed punching no accuracy no power just thing speed and "popping" the bag. And practice bobbing (moving the head down) and slipping (moving the head to the side) to minimize the amount of hits your opponent can land. Make it hard for him.

When running keep your hands and arms in the guard position.

When hitting the bag keep your hands up.

This is a habit that you need to develop so that you are comfortable in this position all of the time.

Most have a bad habit of dropping their hands when fighting, and especially when bringing your arm back from throwing a punch.

My coach used to stand behind me and hit me in the face with a glove when I dropped my hands.

You would be surprised how fast you can learn when properly motivated.

There's no quick fix: just keep hitting the double end and heavy bags (with proper technique) for longer and longer periods and your stamina will gradually improve.

Btw, don't waste your time with the speed bag: trainers like pupils to use them becuz they eat up time and don't require much supervision, allowing clubs to collect your money without teaching you anything useful: when one hits the speed bag, one does so with the SIDE of the hand and standing upright with one's feet "square" to the bag, none of which one does when sparring, shadowboxing, or hitting the other bags. Also, you'll notice that none but the most vainglorious and narcissistic (pro) boxers will waste time learning various speed bag "tricks": check out film of, say, Harry Greb, Ray Robinson, & Muhammad Ali and you'll see that don't waste their time trying to impress people with silly gimmicks.

Speed bad should help also you need to be as relaxed as possible this should make it much easier to keep your hands up.

Whenever Im boxing my arms get tired really fast and I cant keep my hands up. Is there any kind of bag work or exercises that would help with this? I am healthy and have well defined arms, so it's not a strength issue.