Get three guys near your weight and ability level and rotate in, with each man getting back two 3 minute rounds before exiting A vs B then C. Then A rests B vs A then C. Then B rests C vs B than A. Then C rests Repeat this exercise often. Yes, you will be tired, but the best way to increase boxing stamina is to go rounds in the ring. You could be breathing wrong, not relaxing enough, whatever just pay attention to what works and what is not working. You'll find a way to pace your self. The best way to gas yourself is to miss a lot and throw too many combinations.
Spar more often. Run wind sprints. One, Two, and Three minute drills. Our amateurs often spar 4 one minute rounds even tho an actual bout is only 3 one minute rounds. Are older amateurs spar 4 two or three minute rounds. Often stamina issues are due to nerves and poor technique and over aggression. More sparring can help those problems.
Ya. I never had a problem going 2 rounds in the gym for sparring but 2 rounds in a fight would be tough, which is nerves or tension.
Running, Bag work, and sparring itself will help condition you for sparring but the most important thing to not get tired is mental. You need to know how to pace yourself through the rounds, also if you do get tired you need to not let it mentally get to you and fight through it.
I think you should run on a track instead of a road so you can keep records of what you are doing at certain distances and actually see you are getting in better shape by breaking records. Personal records at 400m, 800m, 1k, 2k, 5k etc..Breaking your personal records is very good psychologically too. If you just go run for a certain amount of time you might not be pushing the pace enough to be increasing your conditioning.
Another way I used to condition myself to fight was by doing everything in 3 minute intervals. Some exercises that are killer to do burpees or planks for a full 3 minutes if you can condition yourself to do rounds of those exercise you're conditioned to fight. Again a lot of it is mental when it comes to you're ability to go rounds if at any point you dont want to be in there you're body will begin to panic and fatigue sets in.