It all comes down to endurance...gained over a number of years of steady consistent aerobic work. If you are not doing much aerobic work, now is the time to start.
I know two guys who could never get past 2:02 for the 800m who were solid 5000m runners, and one who was a 1:59 guy.
The 1:59 guy ran 1:59 in HS, ran 15:10 in HS, 9:09 for 3200m in HS. He could run about 55 for 400m and never improved that or his 800m after HS. He went on to run 3:49 for 1500m, 8:11 for 3000m, 13:59 for 5000m, and 29:59 for 10000m.
One of the 2:02 guys was slow as mud at the 400m and eventually got down to 56 for 400m in college (in a practice time trial) which was the same year he ran 2:02 (I think his HS PR was 2:05). He ran in the 9:20s for 3200m in HS, ran 14:59 for 5000m as a freshman in college, and eventually got to 14:35, 8:26 for 3000m, and 29:52 for 10000m before quitting as a college junior. He was a marathon type with not much turnover.
The other 2:02 guy had PRs of 56, 2:05, 4:33, and 9:45 for 400-3200m in HS. He went on to run 8:11 for 3k, 14:15 for 5k, 29:25 for 10k, and 2:14 for the marathon. He trained specifically for the marathon starting at about age 19 and could barely break 60 for 400m but ran 2:02 during that time.
The bottom line is that it takes a lot of endurance training and sacrificing speed gains. Maybe these guys could have run 1:56 for 800m had they been working the speed end but they gave up some speed to be good long runners. So that means if you are running 2:05 off of speed training you should expect that to be a good 5k runner you will lose some potential at 800m. You may switch over to 5k training and improve your 800 a few ticks like these guys did. Who knows?
I can tell you that if you are running 2:05 off of speed and you don't work very very hard on your endurance you will never see 15:00. I could run 2:05 with complete ease but I never got past 15:45 (I wasn't an 800m type by any stretch of the imagination). Many other guys I could clean up on in HS (from 800m through 5k) went on to run low 14's for 5k just by running a lot of consistent miles over 4-5 years.
I'd say the most important factor is getting out the door every single day for at least 45 minutes and preferrably an hour. It may seem like a lot of running but if you are going slow enough you'll get used to it. Then 2 days a week you'll do your intervals/V02 max work/hills and over time you should improve a lot. Unless you are already doing all this...then I guess you just have to be patient and hope that it comes.
Sorry for the rambling post, I'm doing 5 things at once here...