4 Periods In 2 Months? (taking Pill Late)

I've been on birth control since may, but I went off of it for one month about 3 months back. I really enjoy being on it, but I keep taking the pill an hour or two later than normal and getting my period about 1.5 weeks earlier than i'm supposed to. So I keep taking the pill like normal, and then I stop at the end of the pack and get a 2nd period. I don't think losing all this blood can be healthy, even though, none of my periods are anywhere near as heavy now as they used to be... Maybe 4 tampons over the first few days, and then nothing.

When I get my period late, should I start a new pack? Or skip the iron pills and go straight to my next pack when I finish the current one? Thanks!

-rachel