I had an abnormal pap last year and had a colposcopy. Really they just take a closer look at the abnormal cells, and then take some tissue for a biopsy. It did hurt a bit when they took the tissue sample, and I spotted a little bit for a few days.
The terms my gyno used when I asked her what they were looking for were
dysplasia(simply abnormal cells) or
dysplasia (pre-cancerous cells). Turned out that I had metaplasia, which is a result of having HPV (human papilloma virus). The virus might just clear up on its own but I have to go every 6 months just to keep an eye on it.
If a person has dysplasia, then they do a procedure to remove the pre-cancerous cells and then follow up a few months later to make sure they are still gone.
OK, now that I've typed all that, I'm rereading your original post & realize that it sounds like you've already had a colposcopy, so I'm sorry if I'm telling you stuff you already know.
I would see about a second opinion; it sounds like your dr isn't digging too deeply to find out
why you keep having abnormal paps. Try not to stress too much about it (easy for me to say, I know) because chances are it's nothing serious. You are wise to want to get some hard answers, though, and if you feel your doctor isn't working hard enough to get those answers for you, go elsewhere.
Let us know how it turns out; I'll be thinking of you &sending healthy vibes your way.