What is the best way to increase stamina during cardio?
Caveat that of course you should always proceed into working out after checking with a doctor to make sure nothing is wrong that's going to physically harm you:
Go slow and go more often. But other than that - yes, there's an element where you just have to push through. Running in particular is a mental game at LEAST as much, if not more, than a physical game. Your brain will try and defeat you long before your body is actually ready to quit. "But I'm so tired. My feet hurt. My legs hurt. I just want to stop. I just want to walk." If you knuckle down and do not ALLOW yourself to quit, more often than not, you will find you can do amazing things.
I'll be honest, after that last half marathon, I've been reconsidering my whole "YEAH I'M RUNNIN' A FULL!" idea. But I know that I can do it, no matter how much thoughts creep in that tell me I can't. Because my grit is much stronger than my doubt. I'm not saying you need to go out and do a marathon, LOL - but if you put your mind to something and do not allow yourself to quit, great things happen. Don't. Quit. Don't. Quit. Don't. Quit. One word for each step of the foot. I still remember, running that stupid half, I was so hot, sweat was dripping off me with every step, I was thirsty, I thought for sure I was going to die a dry desert death in the middle of the Midwest, I was running up a long hill, I hated running, I couldn't figure out why for the life of me I decided to do this (again), I wanted to walk more than anything in the world, I thought if I just walk, if I can just stop here and walk... "YOU ARE NOT ALLOWED TO WALK," I started screaming in my head. And on nothing but sheer force of will I kept running. It wasn't fast, but it
was running. It was like that for almost four straight minutes. Having a screaming match with myself inside my head. Refusing to let myself quit.
Even outside of running... I can pretty clearly remember some endurance tracks in RIPPED where I start wondering "Why am I here?? I'M GOING TO DIE." The last release of Body Combat had this horrible long track which was practically nothing but five minutes of jump knees. But since I'm in the middle of a class, my stupid pride won't even let me quit, so I keep going. And surprisingly I've never failed to make it through yet.
Strength training will also help you increase your stamina in surprising ways, but you have to push there too. A friend of mine did a lot of cross fit type exercises and last year ran her first 10K without doing a lot of actual running training, and she was like "it was a lot easier than I expected!" because of the gains she made with strength training. Lifting weights makes me a better runner, cycling too.
Final word - if it hurts, stop. But you have to become better at knowing what "hurts" is versus "this is uncomfortable and I would prefer to not be doing this." The former means stop. The latter means buckle down and keep going.
ETA: Forgot, with running of course it's run slower, other types of cardio you can also do modifications. Like instead of jump knees, we were always welcome to just do a high knee. Modify and make it easier if you have to so long as you just don't quit!
ETA2: and now I have that god awful BodyCombat track stuck in my head and it's making me hate myself OH GOD.