If you're not falling a lot, then you're not pushing yourself enough, ergo you won't see much improvement.
Grasping a basic understanding of proper climbing technique is what enables most new climbers to quickly advance in their climbing abilities, but once you have that understanding of climbing principles, then your limitations are mostly physical; you need stronger fingers and core.
If you're topping out at V2, then chances are you're still not very fond of holding onto anything that you can't fit all four pads on and sink up to your second knuckle, you need to get familiar with hanging onto holds that you think are just terrible, namely: small crimps, pinches, and slippery slopers. Most new climbers hate these types of holds, but that's because it takes training and experience in order to know how to approach them, how to hold them without injuring yourself, and what angle you need to hang onto them without popping off, this is where core strength is key, you need a strong core to keep you balance and hold everything together.
Although this is question is rather broad, the general answer would be to spend more time at the climbing gym in the bouldering cave. You can climb a lot harder in the gym than you can outside, because it's a much more controlled environment, and you don't have to worry as much about hurting yourself when you fall. When I went outdoors I was more interested in toping out than I was projecting something hard, and spent more time finishing problems. If I couldn't get it in a few tries, I'd move on, but in the gym I'd project the same problem for months and some I'd only ever top out on once. Some I'd be able to piece together, but never be able to get all the way through them, and they'd eventually get taken down when the holds were cleaned and the cave re-set.
If you want to see quick improvement, you need to be constantly challenging yourself, and trying problems that are way above your grade, dedicated boulderers will spend absurd amounts of time trying to master a single move in a problem, they will train like crazy, with that one single move in mind. Case and point: anyone who has ever tried to climb "Lucid Dreaming" out in Bishop California, it only has two or three moves, but it's a V15 (downgraded from a V16, but the topout is "only" a V7).