I have several thoughts, some or none of them may actually apply. On the limited info given, its tough to tell.
1. Are you sure you're not just lining fish (trout or suckers). What you describe is extremely common in slower areas with a lot of suckers. Of course, one in every 10 or so you do truly hook one and then pull it in by a fin, so that makes it a little easier to figure out whats going on the rest of the time.
2. Gotta be on the hookset. A split second too late, a bad angle, I'm not sure. Personally, I believe starting off indi fishing is the wrong way, it teaches you to use the indi as a crutch, and thus you can have slack in the line between rod tip and indi. I think its better to start fishing close by high sticking without an indicator, and learning to keep the line tight and "feel" bites. Once you get reasonably proficient at this, you can start moving further away, and adding indicators to give you extra distance. But that very same tight line concept without an indicator, is also the proper way to fish with an indicator.
3. If your hookset was fine, then you're letting slack in the line during the fight. Especially if your using barbless, they will throw the hook often if given slack to do so.
4. Could just be the flies. Perhaps dull hooks. Perhaps your fly is crowding the hook? I often have problems like this with glo bugs, for instance. I try to tie them on "top", but if much material is on the bottom the puffiness crowds the hook and leads to misses or poor hooksets.
5. I also have this trouble with big flies on small trout. They hit em just fine, but don't get it in the mouth right or something and I end up losing a lot. The answer is to go to a smaller fly.
6. This happens a lot to me if I'm fishing downstream of my position. Most of the time the fish take upstream or straight out. But if I fish down, let it hang out in the current (dries, streamers, or nymphs), on the hookset, you're pulling it towards the lips, when you want to be pulling it towards the corner of the mouth. If you can fish more out and up, thats better, but sometimes you can't and you just live with it.
7. I have this happen sometimes on last-minute refusals or "light" takes. The fish doesn't fully commit to it. Fly selection, drag, etc. the same factors that your using to get more strikes are the fix, though sometimes fish are just like that and its hard to figure em out.