Especially when they are starting out people tend to place importance on getting through an entire session of yoga without having to lay down on their mats. There is an unconscious element of competition that shows up in just about every activity in our Western society and yoga is not immune to it. Having to take a break can make you feel like a failure and you also might be inclined to compare your skill level to those practicing around you.
This attitude creates unnecessary stress and insures that you will improve at a much slower pace. Probably the biggest reason why is that in order to make it through a whole session you will not do individual asanas at the level they are meant to be performed. Your arms and legs will not be at the proper angles during warrior two for example, because doing so is much harder and will make you run out of steam faster. Obviously you can see the problem, which is that you are learning bad habits and not strengthening the correct muscles to make the poses more doable next time.
There is a simple way to beat this problem, and it is to leave judgments at the door and decide that you are going to do the very best you can on each asana until you can no longer hold it properly and then switch into dead man’s pose without feelings of guilt or failure. Yoga is not just about poses and in fact their primary purpose is to get you into a meditative state in order to discover Self. You can easily do this from the floor by continuing to concentrate on your ujjayi breathing and remaining completely in the moment. In other words, you will still be practicing yoga in every sense of the word even though you have given up on a particular pose.
Actually from a philosophical point of view this attitude is the practice of yoga, and the customary way of going halfway in order to squeak by and appear to others and yourself as if you are capable of getting through your whole practice without taking a break is not yoga. Have the discipline do the very best you can with the skill set and endurance you have right now, take a break without judgment when you can no longer maintain your best, continue to focus on your breath at these times, and you will improve more rapidly while feeling great about your practice.