Are you going directly into your next pill pack and still bleeding? Traditional pill packs contain 28 pills. Only 21 are considered active, as they are the pills that interact with your hormones. The others are the placebo/ inactive pills. For you to skip your period, you have to go immediately into the active pills, so you are still taking pills... If your just skipping the placebo pills and not going into a new pack, it is no different than taking the placebo pill. If you are going immediately into the new pack (the 21 active pills) and still bleeding, then the amount of estrogen your getting in the pills may not be the right amount for you. There are higher and lower dose pills that may be a better fit. Talk to your Dr. about it.. Most Drs. can even address this issue over the phone, especially if it just a matter of swapping pill type. Good Luck
The fact that you skipped your placebo pills and went right to the next set of active pills and still had a period means that this set of hormones is not enough for you to stop getting natural signals from your body to have a period. In your shoes I would be concerned that this means you could have ineffective contraceptive protection. This is definitely something to talk to the doctor about if you are interested in avoiding pregnancy.
Regarding running a couple of cycles worth of active pills together to avoid one period, that is not harmful, but you sound like you're thinking you can skip your period for four months at a time. I wouldn't recommend that. Periods are needed by the uterus. One period skipped (that is, if you find the pills to do it) is no big deal. But assuming you can go on and on and never have a period -- not so healthy for a lot of reasons. So even if your doc gives you a pill that does have the effect that you can skip your period, only do it every now and then.