How long you are able to sustain an activity at a suitable level (while being able to recover from it fairly easily) is what is referred to as your endurance level. Endurance levels are built up via those dedicated to training (particularly maintaining a higher level of cardiovascular fitness) and those with overall optimum health and well-being levels.
What trainers like me are seeing however are individuals working in the wrong way to build that endurance, often running the risk of causing real damage to themselves. There are better ways!
What to Avoid
Do not over-extend yourself while trying to reach high endurance levels. A world class body builder or runner may be able to sustain the pressure and strain of their work out at a higher level and for longer than you but that is to be expected. They have trained for many years to reach such a level, train rigorously and follow a very strict diet and training-focused lifestyle.
If you try to push yourself to levels that you are not ready for you will hurt yourself and badly. Not only are there physical implications to over-extending yourself, there are mental ones too. Constant mental and physical stress when you are unprepared fully for either may cause long-lasting damage and is certainly no good from a motivation perspective.
Be realistic, you are looking to increase your health, not necessarily "beat" someone else's endurance record.
What to Concentrate On
Work to a scaled training plan which looks at gradually and responsibly improving your endurance levels while ensuring that you have time to recover fully and a diet which facilitates just that. High Intensity Interval training (HIIT) allows you to increase your VO2 Max as well as your lactate threshold without causing irreparable damage. Remember that what you are looking at with HIIT is to increase your intensity; how hard you work as opposed to how long for. Trying to push too hard completely undoes what you are training to achieve by choosing HIIT in the first place.
Look too at introducing and adding focus to strength training as well as overall health and fitness as concentrating on one area and one training type alone is counter-productive. A multi-disciplinary approach is best and is what will, again, look to decreasing the risk of damage what boosting your endurance levels
Increasing your endurance levels is something which becomes something of a natural challenge once you have reached a certainly level of proficiency in whatever type of training you favour however it is important to remember that to increase your endurance in that specialty that you need to look at your overall health and fitness levels. This is essential if you are going to enjoy the endurance successes and benefits you are seeking without the journey to achieving them being one which causes you long term and often irreparable damage.