What HIIt are you doing? Some HIIT such as jump roping 20 seconds on 10 seconds off is easier than say, sprinting for 20 seconds jogging for 10? You can start with easier HIIT if you'd like but to improve whatever you're doing...
Stamina comes in the form of aerobic capacity, lactic capacity, alactic capacity, and muscular endurance. They all play a part in any type of cardio, but they come into play at different times. Capacity is the length at which an energy system can last. Generally, alactic energy system lasts 10 to 20 seconds, lactic 30 to 90 seconds, aerobic, 90 seconds plus. The work ratio is also important work-to-rest.
Alactic: 1:10 or 1:5
Lactic: 1:2 or 1:1.
Aerobic:2:1 (or greater, such as 20:1, 30:1,etc)
Doing the math,HIIT is kind of an odd egg and uses a combination iof both aerobic and anaerobic. If uses an aerobic work-to-rest ratio but is mostly anaerobic intensity. If you can only last a few minutes, you might be weak in both. How is your regular cardio, can you jog 20 to 30 minutes straight without rest? If not, I'd suggest adding jogging a few times a week to enhance your aerobic capacity. In addition to this you can try circuit training or metabolic conditioning workouts. Unfortunately if you can only last a few minutes doing HIIT these might be difficult but it'll be easier than HIIT.
To increase your anaerobic, it's mostly the lactic energy system at play. You can do anaerobic exercises such as battle ropes, kettlebell swings, box jumps, jump ropes, etc.. really a high intensity cardio. Avoid sprinting. The exception to HIIT being that you're using the proper work-to-rest ratio. So do a high intensity cardio exercise for 60 seconds, than rest 60 seconds(or 120 if you're weak). Do about 10 sets of that. This could be 60 second jump ropes, etc.. just make sure you are using a high intensity with it.. for example jump rope as much as you can in 60 seconds, don't go at a relaxing pace. Regular weightlifting with a 1:2 work-to-rest ratio can also help.